stats

If the knowledge that an event A has occurred implies that a second event B cannot occur, then the events A and B are said to be

 A. independent.

 B. collectively exhaustive.

 C. the sample space.

 D. mutually exclusive.

mutually exclusive

If event A and event B are mutually exclusive and event A has probability 0.5 and event B has probability 0.2, then the probability that A or B occurs is 

0.7

Government data assign a single cause for each death that occurs in the United States. (Thus, in government terminology, causes of death are mutually exclusive.) In a certain city, the data show that the probability is 0.35 that a randomly chosen death was due to cardiovascular (mainly heart) disease, and 0.25 that it was due to cancer.

(a) The probability that a death was due either to cardiovascular disease or to cancer is

0.6

Government data assign a single cause for each death that occurs in the United States. (Thus, in government terminology, causes of death are mutually exclusive.) In a certain city, the data show that the probability is 0.35 that a randomly chosen death was due to cardiovascular (mainly heart) disease, and 0.25 that it was due to cancer.

(b) the probability that the death was not due to either of these two causes is

0.4

for a particular large group of people, blood types are distributed as shown below. (note that each person is classified as having exactly one of these blood types.)

(a.) the probability that a randomly selected person will have type AB blood is

A. 0.02

B. 0.35

C. 0.16

D. None of the above

0.35

for a particular large group of people, blood types are distributed as shown below. (note that each person is classified as having exactly one of these blood types.)

(b) Maria has type B blood. She can safely receive blood transfusions from people with blood types O and B. What is the probability that a randomly selected person will be able to donate blood to Maria?

 A. 0.18

 B. 0.02

 C. 0.49

 D. None of the above.

0.18

for a particular large group of people, blood types are distributed as shown below. (note that each person is classified as having exactly one of these blood types.)

(c) if two people are selected at random, what is the probability that both people selected will have type O blood

A. 0.32

B. 0.0256

C. 0.16

D. None of the above

0.0256

At a certain high school, if a student is selected at random and asked what they plan to do after graduating, the probability distribution for their response is given above. Determine the following:

(a) P(Attend a junior college)

(b) P(Attend a technical school)

(c) P(Receive training after high school but not at a college)

(a) 0.2

(b) 0.1

(c) 0.2

Choose a student in grades 9 to 12 at random and ask if he or she is studying a language other than English. (You may assume that students are studying at most one language besides English.) Here is the distribution of the students:

(a) What is the probability that a randomly chosen student is, in fact, studying a language other than English?

(b) What is the probability that a randomly chosen student is studying French, German, or Spanish?

(c) What is the probability that a randomly chosen student is studying a language besides English, but not German?

(a) 0.41

(b) 0.38

(c) 0.40

Suppose that, for students who are enrolled in college algebra, 70 percent are freshmen, 46 percent are female, and 28 percent are female and are freshmen. Your answers below should be entered as decimals and rounded to three decimal places.

(a) One student will be selected at random. What is the probability that the selected student will be a freshman or female (or both)?

(b) One student will be selected at random. What is the probability that the selected student will not be a freshman?

(c) Two students will be independently selected at random. What is the probability that both of the selected students will be female?

(a) 0.88

(b) 0.30

(c) 0.2116

In a carnival game, a player spins a wheel that stops with the pointer on one (and only one) of three colors. The likelihood of the pointer landing on each color is as follows: 60 percent BLUE, 20 percent RED, and 20 percent GREEN.

(a) Suppose we spin the wheel, observe the color that the pointer stops on, and repeat the process until the pointer stops on BLUE. What is the probability that we will spin the wheel exactly three times?

(b) Suppose we spin the wheel, observe the color that the pointer stops on, and repeat the process until the pointer stops on RED. What is the probability that we will spin the wheel at least three times?

(c) Suppose we spin the wheel, observe the color that the pointer stops on, and repeat the process until the pointer stops on GREEN. What is the probability that we will spin the wheel 2 or fewer times?

(a) 0.096

(b) 0.64

(c) 0.36

The home states of a certain group of people are distributed as follows: 51 percent are from MISSOURI, 25 percent are from KANSAS, and 24 percent are from IOWA. (No one in the group had a home state other than one of these three.)

Suppose we randomly select a person from this group. What is the expected value of the number of letters in the selected person's home state?

6.54

A phone-in poll conducted by a newspaper reported that 74% of those who called in liked ''reality TV.''

(a) The number 74% is a

A. parameter.

B. statistic.

C. population.

D. sample.

statistic

A phone-in poll conducted by a newspaper reported that 74% of those who called in liked ''reality TV.''

(b) The unknown true percentage of American citizens who like ''reality TV'' is a

 A. sample.

 B. population.

 C. parameter.

 D. statistic.

parameter

The population is

 A. the same thing as a census.

 B. the set of all items of interest.

 C. a parameter.

 D. the collection of items upon which measurements are taken.

the set of all items of interest

An estimator is

A. a statistic that is used to ''guess'' the value of a parameter.

B. a value that is computed using all the measurements in the population.

C. a parameter that is used to ''guess'' the value of a statistic.

D. the same thing as a parameter.

a statistic that is used to “guess” the value of a parameter

The sampling distribution of a statistic is

 A. the population consisting of all the values of the statistic that could be observed based on all possible samples of the correct size.

 B. the mechanism that determines whether or not randomization was effective.

 C. the extent to which the sample results differ systematically from the truth.

 D. the probability that we obtain the statistic in repeated random samples.

the population consisting of all the values of the statistic that could be observed based on all possible samples of the correct size

A measurement is normally distributed with μ=30 and σ=5.9. Round answers below to three decimal places.

(a) The mean of the sampling distribution of x̄ for samples of size 7 is:

(b) The standard deviation of the sampling distribution of x̄  for samples of size 7 is:

(a) 30

(b) 2.230

For patients who have been given a diabetes test, blood-glucose readings are approximately normally distributed with mean 129 mg/dl and a standard deviation 10 mg/dl. Suppose that a sample of 4 patients will be selected and the sample mean blood-glucose level will be computed.

Enter answers rounded to three decimal places.

According to the EMPIRICAL RULE, in 95 percent of samples the SAMPLE MEAN blood-glucose level will be between

the lower-bound of ___and the upper-bound of ___

119; 139

A biologist claims that nearly 45 percent of all Americans have brown eyes. A random sample of n=80 Mizzou students found 32 with brown eyes. Give the numerical value of the statistic p̂.

p̂ =

0.4

Nationwide, 65 percent of persons taking a certain professional certification exam pass. Consider, for a samples of 200, the sampling distribution of p̂. (Each answer should be entered as a proportion rounded to three decimal places.)

(a) The mean of the sampling distribution of p̂ is___

(b) The standard deviation of the sampling distribution of p̂ is: ___

.650; 0.034

A random sample of 80 Mizzou students showed that 24 had driven a car during the day before the survey was conducted. Suppose that we are interested in forming a 99 percent confidence interval for the proportion of all Mizzou students who drove a car the day before the survey was conducted.

Where appropriate, express your answer as a proportion (not a percentage). Round answers to three decimal places.

(a) The estimate is: ____

(b) The standard error is: ____

(c) The multiplier is: ____

(a) 0.3

(b) 0.051

(c) 2.576

A recent survey showed that among 100 randomly selected college seniors, 20 plan to attend graduate school and 80 do not. Determine a 80 % confidence interval for the population proportion of college seniors who plan to attend graduate school. (Enter each answer rounded to three decimal places.)

80 % CI:  ____to ____

0.149 to 0.251

A 90% confidence interval for the mean of a population is computed to be 135 to 160. Which one of the following claims would the interval tend to refute?

 A. The population mean is more than 140.

 B. The population mean is less than 150.

 C. The population mean is more than 110.

 D. The population mean is less than than 125.

 E. The population mean is between 140 and 150.

the population mean is less than 125

A 95% confidence interval for the mean of a population is computed to be 6 to 14. Which one of the following claims would the interval tend to support?

 A. The population mean is less than 15

 B. The population mean is more than 17. 

 C. The population mean is between 8 and 10.

 D. The population mean is more than 7.

 E. The population mean is exactly 9.

the population mean is less than 15

Match the confidence level with the confidence interval for the population mean

1. 80%

2. 68%

3. 99%

A random sample of n=100 observations produced a mean of x̄=31 with a standard deviation of s=8

(a) Find a 99% confidence interval for μ

Lower-bound: ___Upper-bound: ____

(b) Find a 90% confidence interval for μ

Lower-bound: ____Upper-bound: ____

(c) Find a 95% confidence interval for μ

Lower-bound: ____Upper-bound: ____

(a) lower-bound: 28.939 Upper-bound: 33.061

(b) Lower-bound: 29.684 Upper-bound: 32.316

(c)Lower-bound: 29.432 Upper-bound: 32.568

Starting salaries of 64 college graduates who have taken a statistics course have a mean of $42,500 with a standard deviation of $6,800. Find a 68% confidence interval for μ

Lower-bound: ____Upper-bound: _____

41650; 43350

A market research firm supplies manufacturers with estimates of the retail sales of their products from samples of retail stores. Marketing managers are prone to look at the estimate and ignore sampling error. A random sample of 36 stores this year shows mean sales of 80 units of a small appliance with a standard deviation of 7 units. During the same point in time last year, a random sample of 49 stores had mean sales of 72 units with standard deviation 4 units. It is of interest to construct a 95 percent confidence interval for the difference in population means μ1-μ2, where μ1 is the mean of this year's sales and μ2 is the mean of last year's sales.

(a) The estimate is: ____

(b) The standard error is: ____.

(c) The multiplier is : _____.

(a) 8

(b) 1.299

(c) 2.576

A recent survey showed that among 100 randomly selected college seniors, 20 plan to attend graduate school and 80 do not. Determine a 80 % confidence interval for the population proportion of college seniors who plan to attend graduate school. (Enter each answer rounded to three decimal places.)

80% CI: ____ to _____

0.149 to 0.251

A 90% confidence interval for the mean of a population is computed to be 135 to 160. Which one of the following claims would the interval tend to refute?

 A. The population mean is more than 140.

 B. The population mean is less than 150.

 C. The population mean is more than 110.

 D. The population mean is less than than 125.

 E. The population mean is between 140 and 150

The population mean is less than 125

A 95% confidence interval for the mean of a population is computed to be 6 to 14. Which one of the following claims would the interval tend to support?

 A. The population mean is less than 15.

 B. The population mean is more than 17. 

 C. The population mean is between 8 and 10.

 D. The population mean is more than 7.

 E. The population mean is exactly 9

The population mean is less than 15

A random sample of n=100 observations produced a mean of x̄=31 with a standard deviation of s=8

(a) Find a 99% confidence interval for μ

(b) Find a 90% confidence interval for μ

(c) Find a 95% confidence interval for μ

(a) Lower-bound: 28.939 Upper-bound: 33.061

(b) Lower-bound: 29.684 Upper-bound: 32.316

(c) Lower-bound: 29.432 Upper-bound: 32.568

Starting salaries of 64 college graduates who have taken a statistics course have a mean of $42,500 with a standard deviation of $6,800. Find a 68% confidence interval for μ

Lower-bound: ___Upper-bound: ____

41650; 43350

For students at a large, state university, consider two groups. Group 1: Students who purchased their textbooks for the current semester at the campus bookstore and Group 2: Students who purchased their textbooks for the current semester online. A 99% confidence interval for μ1-μ2, the difference in population mean amounts spent on textbooks, is 30 to 60 dollars.

1. The confidence interval provides no strong evidence to support or refute the claim that, on average, students who purchased their books at the campus bookstore spent __________ dollars more than those who purchased their books online.

 A. at least 20

 B. more than 25

 C. less than 65

 D. at most 70

 E. more than 50

more than 50

For students at a large, state university, consider two groups. Group 1: Students who purchased their textbooks for the current semester at the campus bookstore and Group 2: Students who purchased their textbooks for the current semester online. A 99% confidence interval for μ1-μ2, the difference in population mean amounts spent on textbooks, is 30 to 60 dollars.

2. The confidence interval would tend to support the claim that, on average, students who purchased their books at the campus bookstore spent __________ dollars more than those who purchased their books online.

 A. at most 40

 B. less than 20

 C. more than 65

 D. at least 25

 E. at least 32

at least 25

The null hypothesis is

 A. assumed to be true unless substantial evidence to the contrary is presented.

 B. the same thing as the ''research hypothesis.''

 C. a statement that the data are all 0.

 D. the probability of observing the data you actually obtained

assumed to be true unless substantial evidence to the contrary is presented.

In testing hypotheses, which of the following would tend to be evidence in favor of the alternative hypothesis?

 A. A small p -value.

 B. A small level of significance.

 C. A large level of significance.

 D. A large p -value.

a small p-value

The p -value of a hypothesis test is

 A. the probability the null hypothesis is false.

 B. The probability of observing evidence in favor of the alternative hypothesis as strong or stronger than that which was observed if the null hypothesis were true.

 C. the probability the null hypothesis is true.

 D. The probability of observing evidence in favor of the null hypothesis as strong or stronger than that which was observed if the alternative hypothesis were true.

The probability of observing evidence in favor of the alternative hypothesis as strong or stronger than that which was observed if the null hypothesis were true.

For each statement, select the correct null hypothesis, H0, and alternative hypothesis, HA, in symbolic form.

(a) A certain type of hummingbird is known to have an average weight of 4.55 grams. A researcher believes that hummingbirds (of this same type) living in the Grand Canyon differ in weight from the population as a whole. The researcher finds a sample of 30 such hummingbirds from the Grand Canyon and calculates their average weight to be 3.75 grams. (Here μ represents the population mean weight of hummingbirds who live in the Grand Canyon.)

H0: μ=4.55, HA: μ≠4.55

For each statement, select the correct null hypothesis, H0, and alternative hypothesis, HA, in symbolic form.

(b)The mean height of all adult American males is 69 inches (5 ft 9 in). A researcher wants to prove that young American males between the ages of 18 and 21 tend to be taller than 69 inches. A random sample of 100 young American males ages 18 to 21 yielded a sample mean of 71 inches. (Here μ represents the population mean height of young American males.)

H0: μ=69, HA: μ>69

For each statement, select the correct null hypothesis, H0, and alternative hypothesis, HA, in symbolic form.

(c) According to the Merck Veterinary Manual, the average resting heart rate for a certain type of sheep dog is 115 beats per minute (bpm). A Montana farmer notices his aging sheep dog has been acting more lethargic than usual. He believes that her heart rate is slower than normal for her breed. The farmer measured the dog's heart rate on 15 occasions and found a sample mean heart rate of 110.2 bpm. (Here μ represents the mean heart rate of the farmer's sheep dog over all occasions.)

H0: μ=115, HA: μ<115

In a particular municipality, it is believed that 25 percent of homes are not properly insulated. In order to test H0: p=.25 vs. HA: p≠.25 (where p is the population proportion of homes that are not properly insulated) a random sample of 300 homes was selected. In the sample, it was found that 108 homes were not properly insulated. If the null hypothesis is true, then the z-score for the sample proportion is: 

4.4

A consumer believes that a certain potato chip maker is putting fewer chips in their regular bags of chips than the advertised amount of 12 ounces. In order to test the null hypothesis that the average chip weight is 12 ounces per bag vs. the alternative hypothesis that the average chip weight is less than 12 ounces per bag, a random sample of 37 bags were selected. The resulting data produced a p - value of 0.09.

(a) At a 5% level of significance, should the null hypothesis be rejected? (Type: Yes or No): 

(b) At a 10% level of significance, should the null hypothesis be rejected? (Type: Yes or No)

(a) no

(b) yes

In a statistical test of hypotheses, saying that ''the evidence is statistically significant at the .05 level'' means

 A. α=.10

 B. the p - value is less than .05.

 C. α is more than .25.

 D. the p-value is at least .05.

the p-value is less than .05

For each situation, state the null and alternative hypotheses

(a) The diameter of a spindle in a small motor is supposed to be 3.6 millimeters (mm) with a standard deviation of 0.12 mm. If the spindle is either too small or too large, the motor will not work properly. The manufacturer measures the diameter in a sample of 42 spindles to determine whether the mean diameter has moved away from the required measurement. Suppose the sample has an average diameter of 3.55 mm.

H0: μ=3.6, HA: μ≠3.6

for each situation, state the null and alternative hypotheses

(b) Harry thinks that prices in Caldwell, Idaho, are higher than the rest of the country. He reads that the nationwide average price of a certain brand of laundry detergent is $22.85 with standard deviation $1.95. He takes a sample from 38 local Caldwell stores and finds the average price for this same brand of detergent is $21.59

H0: μ=22.85, HA: μ>22.85

The fill volume of a random sample 33 cans of Coke were found to have a mean of x̄=12.15 with standard deviation of s=0.1 Find the value of the test statistic z for evaluating the null hypothesis μ=12

z=8.616

Find the P - value for the test statistic z=-1.41 for the following null and alternative hypotheses:

H0: The population mean is 50.

HA: The population mean is less than 50.

The P - value is____

0.08

Find the P - value for the test statistic z=-1.41 for the following null and alternative hypotheses:

H0: The population mean is 50.

HA: The population mean is not equal to 50.

The P - value is___

0.16

An article published in the Washington Post claims that 45 percent of all Americans have brown eyes. A random sample of n=84 college students found 31 who had brown eyes.

Consider testing

H0: p=.45

HA: p≠.45

The test statistic is z = ______

p-value: ____

z=-1.491

p-value: 0.14

A random sample of n=1200 registered voters and found that 620 would vote for the Republican candidate in a state senate race. Let p represent the proportion of registered voters who would vote for the Republican candidate.

Consider testing

H0: p=.50

HA: p>.50

The test statistic is z= ____

Regardless of what you actually computed, suppose your answer to part (a) was z = 1.28. Using this z, p-value =____

z = 1.155

p-value = 0.1

The t statistic for a test of 

H0: μ=35

HA: μ<35

Based on n=10 has the value t=-1.61

(a) what are the degrees of freedom?

(b)  Using the appropriate table in your formula packet, bound the p-value as closely as possible: ___ < p-value < ___

(a) 9

(b) 0.067 < p-value < 0.084

The t statistic for a test of 

H0: μ=32

HA: μ>32

Based on n=17 has the value t=1.93

(a) what are the degrees of freedom? ____

(b)  Using the appropriate table in your formula packet, bound the p-value as closely as possible: ____< p-value < ____

(a) 16

(b) 0.031 < p-value < 0.045

The t statistic for a test of 

H0: μ=14

HA: μ≠14

Based on n=6 has the value t=-1.1

(a) what are the degrees of freedom? ___

(b)  Using the appropriate table in your formula packet, bound the p-value as closely as possible: ____ < p-value <____

(a) 5

(b) 0.256 < p-value < 1.000

Dan thinks a certain potato chip maker is putting less product in their personal-sized bags of chips. In the past, these bags contained one ounce of product. Dan conducted a test of H0: μ=1 vs. HA: μ<1. From a random sample of 22 bags of potato chips he calculated a p-value of 0.056 for the sample

a) At a 5% level of significance, is there evidence that Dan is correct? (Type Yes or No): ____

(b) At a 10% level of significance, is there evidence that he is correct? (Type Yes or No):____

a) no

b) yes

Katie thinks that people living in a rural environment have a healthier lifestyle than other people. She believes the average lifespan in the USA is 77 years. A random sample of 20 obituaries from newspapers from rural towns in Idaho give x̄=80.7 and s=0.88 Does this sample provide evidence that people living in rural Idaho communities live longer than 77 years?

State the null and alternative hypotheses: ______

Find the test statistic t = ____

H0: μ=77, HA: μ>77

t=18.803

The hemoglobin count (HC) in grams per 100 milliliters of whole blood is approximately normally distributed with a population mean of 14 for healthy adult women. Suppose a particular female patient has had 15 laboratory blood tests during the past year. The sample readings showed an average HC of 17.86 with a standard deviation of 1.18. Does it appear that the population average HC for this patient is not 14?

state the null and alternative hypotheses: ____

Find the test statistic, t = ____

H0: μ=14, HA: μ≠14

t= 12.669

In a hypothesis testing context, before examining the data, one should

 A. decided whether the alternative hypothesis is one-sided or two-sided.

 B. compute the p-value for the test.

 C. decide whether or not to reject the null hypothesis.

 D. All of the above.

decided whether the alternative hypothesis is one-sided or two-sided.

In general, there is more information provided by .

 A. a confidence interval than a p-value.

 B. a p-value than a confidence interval.

 C. a sample statistic than a confidence interval for the corresponding parameter.

 D. All of the above.

a confidence interval than a p-value.

Among dogs in a certain large city, 77 percent were adopted from an animal shelter. Suppose that two dogs will be independently selected at random.

The probability that BOTH selected dogs will have been adopted from an animal shelter is __________ .

 A. 0.3557

 B. 0.5929

 C. 0.7965

 D. 0.864

 E. 0.4743

0.5929

Suppose that 64 percent of American adults know how to play checkers. American adults will be selected at random, one at a time, until someone who knows how to play checkers is selected.

The probability that more than 2 people will be selected is __________ .

 A. 0.1296

 B. 0.6518

 C. 0.5648

 D. 0.0778

 E. 0.1037

0.1296

In a game of chance, a fair coin is flipped twice and the outcome determines the amount of money the player wins as shown in the table below. (For reference, the probability of each outcome is provided.)

If you are permitted to play this game one time for free, the expected value of the amount you will win is __________ dollars.

 A. 15

 B. 11

 C. 3

 D. 27

 E. 7

15

Suppose that event A has P(A) = 0.26 and event B has P(B) = 0.45. If these two events are mutually exclusive then __________.

 A. P(A and B) = 1

 B. P(A and B) = 0

 C. P(A|B) = P(A)

 D. P(A and B) = P(A)P(B)

 E. P(A or B) = P(A)

P(A and B) = 0

Each time an attempt is made to start a particular old car, there is a 0.58 probability that the car will successfully start. Attempts will be made repeatedly until the car starts.

The probability that 2 or fewer attempts will be needed to start the car is __________ .

 A. 0.6589

 B. 0.9118

 C. 0.3294

 D. 0.8236

 E. 0.9412

0.8236

Freshmen at a particular university take one of three math classes:

12 percent take calculus for 5 credit hours

41 percent take college algebra for 3 credit hours

47 percent take trigonometry for 2 credit hours.

If a freshman is selected at random, the expected value of the number of credit hours of their math class is __________ .

 A. 2.216

 B. 1.108

 C. 2.77

 D. 3.878

 E. 3.324

2.77

Of high school juniors from a particular school district, 0.27 proportion have a driver's license, 0.38 proportion are enrolled in an online course, and 0.082 proportion have driver's license AND are enrolled in an online course.

The probability that a randomly selected junior will have a driver's license OR be enrolled in an online course (or both) is __________ .

 A. 0.341

 B. 0.784

 C. 0.227

 D. 0.827

 E. 0.568

0.568

For a particular large group of people, blood types are distributed as shown below. (Note that a particular person may only have one blood type, meaning that blood types are mutually exclusive.)

A person who has type B blood can safely receive blood transfusions from people whose blood type is either O or B. If a person is selected at random, what is the probability that the selected person will be able to safely donate blood to a person with type B blood?

 A. 1

 B. 0.23

 C. 0.08

 D. 0

 E. 0.52

0.23

Of students at a particular large university, 0.8 proportion are in-state residents and 0.28 proportion are sophomores. You may assume that being an in-state resident and being a sophomore are independent. One student will be selected at random.

The probability that the selected student will be an in-state resident OR a sophomore (or both) is __________ .

 A. 0.856

 B. 0.685

 C. 0.928

 D. 0.942

 E. 0.952

0.856

In a particular school district, 52.1 percent of high school seniors have a driver's license. A high school senior will be selected at random from among those attending this district.

The probability that the selected student will NOT have a driver's license is __________ .

 A. 0.192

 B. 0.287

 C. 0.479

 D. 0.826

 E. 0.74

0.479

NOTE: Boone County is located in the State of Missouri.

Suppose we randomly select a Mizzou student. If the probability of selecting a student who was born in the State of Missouri is 0.77, then the probability of selecting a student who was born in Boone County must be __________ .

 A. greater than 0.77

 B. exactly 0.77

 C. exactly 0.23

 D. less than or equal to 0.77

 E. None of the above

less than or equal to 0.77

Among students receiving a particular scholarship, 56 percent are juniors. Suppose that scholarship recipients are randomly selected, one at a time, until a junior is selected.

The probability that exactly 2 scholarship recipients will be selected is __________ .

 A. 0.7488

 B. 0.6232

 C. 0.1971

 D. 0.0986

 E. 0.2464

0.2464

Select the correct null hypothesis, H0, and alternative hypothesis, HA, in symbolic form.

According to the highway patrol, the population mean speed of cars on a particular highway during rush hour is 42 mph. A motorist believes the population mean speed is lower. The motorist randomly selected a sample of n=52 cars during rush hour and found them to have an average speed of x̄=39 mph with a standard deviation of s=5 mph.

The hypotheses the motorist is interested in testing are:

H0: μ=42, HA: μ<42

When a particular hypothesis testing procedure is applied to a case for which H0 is true, the probability that the test will reject H0 is 0.07 and the probability that the test will accept H0 is 0.93.

This information means that 

 A. confidence level = 0.07

 B. Power = 0.93

 C. α=0.07

 D. β=0.07

 E. α=0.93

α=0.07

Suppose that, the population proportion of homeowners who have considered purchasing solar panels is p=0.3. For samples of size n=84, consider the sampling distribution of p̂=sample proportion of homeowners who have considered purchasing solar panelsFor samples of size n=84, the MEAN of the sampling distribution of p̂ is __________ .

 A. 0.35

 B. 0.25

 C. 0.4

 D. 0.3

 E. None of the above

0.3

Suppose that, for adults in a particular state, the population proportion who own a home is p=0.8. Consider the sampling distribution of p̂=sample proportion who own a home for samples of n=64.

According to the empirical rule, approximately 99.7 percent of samples of size n=64 will produce a p̂ between __________.

 A. 0.625 and 0.975

 B. 0.65 and 0.95

 C. 0.675 and 0.925

 D. 0.7 and 0.9

 E. 0.75 and 0.85

0.65 and 0.95

For travellers visiting a particular large city, a 95% confidence interval for μ= the population mean cost of a ride-share from the airport to downtown is 60 to 63 dollars.

The confidence interval would tend to refute the claim that the population mean is __________ dollars.

 A. at most 53

 B. at least 55

 C. less than 67

 D. more than 57

 E. None of the above

at most 53

A sample of n=64 was selected. The sample showed a mean of 77.7 with a standard deviation of 35.52. For a 68 percent confidence interval for μ, the value of the multiplier is __________.

 A. 1

 B. 77.7

 C. 4.44

 D. 35.52

 E. 68 percent

1

A sample of n=64 was selected. The sample showed a mean of 75 with a standard deviation of 38.72.For a 90 percent confidence interval for μ, the value of the estimate is __________.

 A. 38.72

 B. 4.84

 C. 75

 D. 90 percent

 E. 1.645

75

In order to estimate p=the proportion of college students who have their own bathroom, a sample of n=150 was selected. In the sample, 112 college students had their own bathroom. 

For a 99.7 percent confidence interval for p, the value of the standard error is __________.

 A. 0.747

 B. 99.7 percent

 C. 0.036

 D. 150

 E. 3

0.036

(This question is designed to test your understanding of the difference between the standard deviation of a sampling distribution and a standard error that would be used in forming a confidence interval.)

While unknown to researchers, a measurement applied to a particular population is normally distributed with population mean μ=76.2 and population standard deviation σ=30.3 A sample of size n=100 was observed and it was found to have sample mean x̄=70.3 and sample standard deviation s=11.3.

For forming a confidence interval for μ, the standard error is __________.

 A. 1.13

 B. 30.3

 C. 70.3

 D. 3.03

 E. 11.3

1.13

For a particular population, a measurement is normally distributed with mean μ=61.2 and standard deviation σ=32.89. For samples of size n=121, the standard deviation of the sampling distribution of x̄ is __________.

 A. 61.2

 B. 121

 C. 2.99

 D. 32.89

 E. 11

2.99

For a particular breed of cat, a 90% confidence interval for μ=the population mean lifespan is 19 to 22 years. The confidence interval would tend to support the claim that the population mean is __________ years.

 A. more than 16

 B. at most 12

 C. less than 15

 D. at least 29

 E. None of the above

more than 16

Suppose that a measurement on a particular population follows a normal distribution with a mean of μ=170 with a standard deviation of σ=52. Consider the sampling distribution of 

x̄ for samples of size n=169.

According to the empirical rule, approximately __________ percent of samples of size n=169 will produce an x̄ between 166 and 174.

 A. 95

 B. 99.7

 C. 80

 D. 68

 E. 90

68

Select the correct null hypothesis, H0, and alternative hypothesis, HA, in symbolic form.

A coach claims that the population mean resting pulse rate of football players is 60 beats per minutes. In order to prove the population mean is more than what the coach claims, a sample of 

n=91 football players was selected. The sample showed a sample mean resting pulse rate of x̄=64 beats per minute with a standard deviation of s=7.6 beats per minute.

The test of interest is:

H0: μ=60, HA: μ>60

Select the correct null hypothesis, H0, and alternative hypothesis, HA, in symbolic form.

A pet expert claims that the population proportion of pet owners who own a dog is 0.42. A skeptic believes that the population proportion is less than what the pet expert claims. The skeptic selected a sample of n=100 pet owners and found that the sample proportion who own a dog is p̂=0.38.

The test of interest is:

H0: p=0.42, HA: p<0.42

Select the correct null hypothesis, H0, and alternative hypothesis, HA, in symbolic form.

Ages of students on two university campuses were compared. In particular, it was of interest to show that μ1(the population mean age of students on campus 1) was not equal to μ2(the population mean age of students on campus 2).

For campus 1, a sample of n1=83 students was found to have a mean age of x̄1=30 with a standard deviation of s1=1.7 .

For campus 2, a sample of n2=102 students was found to have a mean age of x̄2=26 with a standard deviation of s2= 3.9.

The test of interest is:

H0: μ1-μ2=0, HA: μ1-μ2≠0

In order to test H0:μ=29 vs. HA:μ≠29 at the α=0.01 level of significance, a sample of size n=115 was selected. (NOTE that it says not equal to.)

If the test statistic were z=1.04, then the p-value = __________ .

 A. 0.6

 B. 0.3

 C. 0.85

 D. 0.15

 E. 0.075

0.3

Compute the test statistic H0: μ1-μ2=0, HA: μ1-μ2<0 using the =0.05 level of significance. 

Sample 1: n1=50, x̄1=420.678, and s1=10

Sample 2: n2=50, x̄2=424, and s2=10

Note that: 

The test statistic is z = __________ .

 A. -1.661

 B. -2.159

 C. -1.329

 D. -3.322

 E. -0.332

-1.661

Select the correct null hypothesis, H0, and alternative hypothesis, HA, in symbolic form.

According to a government agency, the population mean age of workers in a particular industry is 31 years. A manager in that industry believes the population mean age is greater than 31. The manager selected a sample of n=75 workers and found the sample to have a mean age of   x̄=34 years with a standard deviation of s=1.3 years.

The hypotheses the manager is interested in testing are:

H0: μ=31, HA: μ>31

For the purpose of testing H0: μ=37, HA: μ>37 at the =0.10 level of significance, data was collected and analyzed. 

For which one of the following values of the p-value would the conclusion of the test be to ACCEPT H0

 A. p-value = 0.072

 B. p-value = 0.037

 C. p-value = 0.054

 D. p-value = 0.028

 E. p-value = 0.172

p-value = 0.172

In order to test H0: p=0.3, HA: p>0.3 a the =0.01 level of significance, a sample of size n=170 was selected. If the test statistic were z=1.23 then the p value=____

 A. 0.11

 B. 0.89

 C. 0.22

 D. 0.0275

 E. 0.055

0.11

This problem asks you to compute the test statistic for a test of H0:p=.05 vs HA:p≠0.5 using the =0.01 level of significance. A sample of n=100 produced p̂=0.55

Note that: 

The test statistic is z = __________ .

 A. 1.7

 B. 0.5

 C. 2

 D. 0.8

 E. 1

1

For the purpose of testing H0: p=0.51, HA: p<0.51 at the α=0.10 level of significance, data was collected and analyzed. 

For which one of the following values of the p-value would the conclusion of the test be to reject H0

 A. p-value = 0.085

 B. p-value = 0.278

 C. p-value = 0.321

 D. p-value = 0.495

 E. p-value = 0.133

0.085

This problem asks you to compute the test statistic for a test of H0: μ=245, HA: μ<245 using the α=0.01 level of significance. A sample of n=100 produced x̄=228.5 and s=50

The test statistic is z = __________ .

 A. -4.29

 B. -5.61

 C. -6.6

 D. -2.64

 E. -3.3

-3.3

In order to test H0: μ1-μ2=0 vs HA: μ1-μ2<0 at the α=0.01 level of significance, two independent, random samples were selected. The sizes of the samples were n1=105 and n2=189

If the test statistic were z=-2.05, then the p-value=____

A. 0.01

 B. 0.02

 C. 0.005

 D. 0.98

 E. 0.04

0.02

In order to test H0: μ=74, HA: μ≠74, a sample size of n=7 was selected and used to compute a test statistic of t=-2.22

If we use the appropriate table in the course formula packet to bound the p-value as closely as possible, the bounds are:

 A.   0.058 < p-value < 0.092

 B.   0.042 < p-value < 0.074

 C.   0.048 < p-value < 0.080

 D.   0.044 < p-value < 0.075

 E.   0.146 < p-value < 0.184

0.058 < p-value < 0.092

In order to test H0: μ=41, HA: μ<41, a sample size of n=15 was selected and used to compute a test statistic of t=-1.56

If we use the appropriate table in the course formula packet to bound the p-value as closely as possible, the bounds are:

 A.   0.061 < p-value < 0.078

 B.   0.058 < p-value < 0.075

 C.   0.071 < p-value < 0.089

 D.   0.060 < p-value < 0.077

 E.   0.055 < p-value < 0.072

  0.061 < p-value < 0.078

In order to test H0: μ=21, HA: μ≠21, a sample size of n=9 was selected and used to compute a test statistic of t=1.37

If we use the appropriate table in the course formula packet to bound the p-value as closely as possible, the bounds are:

 A.   0.172 < p-value < 0.236

 B.   0.208 < p-value < 0.270

 C.   0.168 < p-value < 0.232

 D.   0.178 < p-value < 0.242

 E.   0.164 < p-value < 0.230

0.172 < p-value < 0.236

In order to test H0: μ=8, HA: μ<8, a sample size of n=23 was selected and used to compute a test statistic of t=-1.53

If we use the appropriate table in the course formula packet to bound the p-value as closely as possible, the bounds are:

 A.   0.069 < p-value < 0.086

 B.   0.064 < p-value < 0.081

 C.   0.120 < p-value < 0.136

 D.   0.071 < p-value < 0.089

 E.   0.057 < p-value < 0.074

0.057 < p-value < 0.074