AP stats review

The statistic p estimates:

P

Lila and Robert attend different high schools. They will estimate the population

percentage of students at their respective schools who have seen a certain movie. Lila

and Robert each select a random sample of students from their respective schools and

use the data to create a 95 percent confidence interval. Lila’s interval is (0.30,0.35), and

Robert’s interval is (0.27,0.34). Which of the following statements can be concluded

from the intervals?

Lila’s sample size is most likely greater than Robert’s.

A recent SRS by a regional polling firm in California found that 53% of state residents

support increased investment in water infrastructure. The survey was conducted over

six days and interviewed 520 residents of the state. Which represents the mean and

standard deviation of the sample proportion?

The mean is 0.53, and the standard deviation is sq(0.53)(0.47)/520

Which of the following pairs of sample size n and population proportion p would

produce the greatest standard deviation for the sampling distribution of a sample

proportion p̂ ?

n=250 and p close to 0.5

For a one-sample test for a population proportion p and sample size n, why is it

necessary that nnpp aa aa nn(1 − pp) are both at least 10?

The sample size must be large enough to support an assumption that the sampling

distribution of the sample proportion is approximately normal.

City R is a large city with 4 million residents, and City S is a smaller city with 0.25 million

residents. Researchers believe that the proportion of City S residents who regularly ride

bicycles is between 10 percent and 25 percent and the proportion of City R residents

who regularly ride bicycles is between 20 percent and 50 percent.

Suppose two independent random samples of residents from each city will be taken

and the proportion of residents who ride bicycles is recorded. Based on the population

proportions of residents who regularly ride bicycles, which of the following sample

sizes is large enough to guarantee that the sampling distribution of the difference in

sample proportions will be approximately normal?

50 in City R and 100 in City S

Researchers investigating a new drug selected a random sample of 200 people who are

taking the drug. Of those selected, 76 indicated they were experiencing side effects

from the drug. If 5,000 people took the drug, which of the following is closest to the

interval estimate of the number of people who would indicate they were experiencing

side effects from the drug at a 90 percent level of confidence?

(1620, 2180)

Which of the following is not a condition for constructing a confidence interval to

estimate the difference between two population proportions?

The data must come from populations with approximately normal distributions.

Paul will select a random sample of students to create a 95 percent confidence interval

to estimate the proportion of students at his college who have a tattoo. Of the

following, which is the smallest sample size that will result in a margin of error of no

more than 5 percentage points?

385

Consider a 90 percent confidence interval for a population proportion p. Which of the

following is a correct interpretation of the confidence level 90 percent?

In repeated samplings with the same sample size, approximately 90 percent of the

intervals created will capture the population proportion p.

certain statistic will be used as an unbiased estimator of a parameter. Let M

represent the sampling distribution of the estimator for samples of size 100, and

let N represent the sampling distribution of the estimator for samples of size 200.

b. pp̂(100) ≈ pp̂(200) and σ(100) > σ (200)

12.Which of the following conditions will create a biased estimator of a population

parameter?

The expected value of the estimator is not equal to the population parameter.

13.A polling organization asks an SRS of 1250 high school students many hours of

homework they have on average per night. Suppose that 43% of all students have three

hours of homework per night, on average. Find the probability that the random sample

of 1250 high school students will give a result within 2 percentage points of the true

value?

0.90

14.A large-sample 98 percent confidence interval for the proportion of hotel reservations

that are canceled on the intended arrival day is (0.048, 0.112). What is the point

estimate for the proportion of hotel reservations that are canceled on the intended

arrival day from which this interval was constructed?

0.064

15.A 95 percent confidence interval for the proportion of parents who use parental

controls for blocking, filtering, or monitoring their teenagers’ online activities

is (0.36,0.42).

Which of the following could be a 99 percent confidence interval based on the same

data?

c. (0.36, 0.48)

16.Consider a 90 percent confidence interval to estimate a population proportion that is

constructed from a sample proportion of 66 percent. If the width of the interval is 10

percent, what is the margin of error?

b. 5 percent

17.A random sample of 80 people was selected, and 22 of the selected people indicated

that it would be a good idea to eliminate the penny from circulation. What is the 99

percent confidence interval constructed from the sample proportion pp̂?

0.275 ± 2.576 sqr(0.275)(0.725)/80

In 1960 sociologists studied a random sample of 1,018 families that consisted of a

husband, a wife, and at least one child. Of those families, 5.8 percent reported that the

wife was the primary wage earner of the family. In 2011 the study was replicated with a

random sample of 1,013 families that consisted of a husband, a wife, and at least one

child. Of those families, 22.3 percent reported that the wife was the primary wage

earner of the family. Which of the following represents a 99 percent confidence interval

for the difference between the proportions of families that consisted of a husband, a

wife, and at least one child from 1960 to 2011 that would have reported the wife as the

primary wage earner?

(0.223 − 0.058) ± 2.576�(0.223)(0.777)

1,013

+ (0.058)(0.942)

In order to make statistical inferences when testing a population proportion p, which of

the following conditions verify that inference procedures are appropriate?

I. The data are collected using a random sample or random assignment.

II. The sample size is less than 10 percent of the population size.

III. np≥10 and n(1−p)≥10 for sample size n and hypothesized proportion p.

e. I, II and III

20.Researchers are studying populations of two squirrels, the eastern gray and the

western gray. For the eastern gray squirrel, about 22 percent of the population weighs

over 0.5 kilogram (kg). For the western gray squirrel, about 36 percent of the population

weighs over 0.5 kg. A random sample of 60 squirrels will be selected from the

population of eastern gray squirrels, and a random sample of 120 squirrels will be

selected from the population of western gray squirrels. What is the mean of the

sampling distribution of the difference in sample proportions (eastern minus western)?

e. 0.36 – 0.22

The local ranger station tracked and tagged 2,844 adult female black bears in a national

park. A random sample of 9 adult female black bears from those tagged had an average

body weight of 203 pounds with standard deviation 25 pounds. Which of the following is

a point estimate for the population mean weight of all female black bears that are

tagged?

203

A random sample of 10 employees of a company was selected to estimate the mean

one-way commute time for all employees at the company. The mean and standard

deviation of the sample were 38 minutes and 6 minutes, respectively.

Assuming all conditions for inference are met, which of the following is the margin of

error, in minutes, for a

1.833 (6/sqr10)

The director of fitness for a large corporation with over 5,000 employees recorded the

resting heart rate, in beats per minute (bpm), for 35 employees who were known to

wear activity trackers. The following boxplot summarizes the results.

The director wants to estimate the resting heart rate for all employees with a

confidence interval. Have all conditions for inference been met?

No, the distribution of the sample data is not approximately symmetric.

A large company is considering opening a franchise in St. Louis and wants to estimate

the mean household income for the area using a simple random sample of households.

Based on information from a pilot study, the company assumes that the standard

deviation of household incomes is σ = $7,200. Of the following, which is the least

number of households that should be surveyed to obtain an estimate that is within

$200 of the true mean household income with 95 percent confidence?

b. 1,300

Alicia would like to know if there is a difference in the average price between two

brands of shoes. She selected and analyzed a random sample of 40 different types of

Brand A shoes and 33 different types of Brand B shoes. Alicia observes that the boxplot

of the sample of Brand A shoe prices shows two outliers. Alicia wants to construct a

confidence interval to estimate the difference in population means.

Is the sampling distribution of the difference in sample means approximately normal?

b. Yes, because for each brand it is reasonable to assume that the population size is

greater than ten times its sample size.

Stock market investing is usually conducted by active portfolio management, or the

purchasing and selling of individual company shares, and long-term portfolio

management, or the purchasing of mutual funds for long durations that are made up of

numerous company shares.

According to the central limits theorem, which strategy would have the normally

distributed rate of return?

Long-term portfolio management, because most mutual funds contain more than

thirty individual company shares.

A national consumer agency selected independent random samples of 45 owners of

newer cars (less than five years old) and 40 owners of older cars (more than five years

old) to estimate the difference in mean dollar cost of yearly routine maintenance, such

as oil changes, tire rotations, filters, and wiper blades. The agency found the mean

dollar cost per year for newer cars was $195 with a standard deviation of $46. For older

cars, the mean was $286 with a standard deviation of $58.

Which of the following represents the standard deviation of the sampling distribution of

the sample means?

sqr of 46/45 + 58/40

The mean height of a teenager in the United States in 2022 was 67.5 inches (US

Department of Health) with a standard deviation of 2.5 inches.

Find the probability that the mean height of an SRS of 10 American teenagers will be

less than 65.5 inches?

0.005

According to the central limits theorem, which of the following sample sizes of the

sample mean would most likely produce a sampling distribution closely approximating

normal, assuming all do not violate the 10% condition?

30

10. Further breaking down question 8: the mean height of female American teenagers is 66

inches, and the mean height of male American teenagers is 69 inches. Both have a

standard deviation of 2.5 inches.

d. 1.75

Consider a population with population proportion p, and a sample from the

population with sample proportion ̂p. Which of the following describes the purpose

of the one-sample z-test?

d. To estimate the probability of observing a value as extreme as ̂p given p.

The germination rate is the rate at which plants begin to grow after the seed is

planted. A seed company claims that the germination rate for their seeds is 90

percent. Concerned that the germination rate is actually less than 90 percent, a

botanist obtained a random sample of seeds, of which only 80 percent germinated.

What are the correct hypotheses for a one-sample z-test for a population

proportion p?

c. HH0: pp = 0.90; HHaa: pp < 0.90

In order to make statistical inferences when testing a population proportion p,

which of the following conditions verify that inference procedures are appropriate?

I. The data are collected using a random sample or random assignment.

II. The sample size is less than 10 percent of the population size.

III. np0≥10 and n(1−p0)≥10 for sample size n and hypothesized proportion p0.

e. I, II and III

A recent study indicated that 17 percent of adults in the country actively seek out

science news sites to keep current on topics in science. A university researcher

believes that percent is too low. From a random sample of adults in the country, the

researcher found that 22 percent of the sample actively seek out science news

sites. Which of the following is the most appropriate method for the researcher’s

study?

e. A one-sample z-test for a population proportion.

Approximately 38 percent of people living in Region W have the blood type O

positive. A random sample of 100 people from Region X revealed that 35 people in

the sample had the blood type O positive. Consider a hypothesis test to investigate

whether the percent of people in Region X with O positive blood is different from that

of in Region W. Which of the following is the appropriate null hypothesis for the

investigation?

d. H0: p = 0.38

In a population of bats living in a certain region, 30 percent have a wingspan greater

than 10 inches. In a random sample of 80 bats living outside of the region, 20 had a

wingspan greater than 10 inches. Consider a one-sample z-test to investigate

whether there is evidence that the proportion of bats with a wingspan greater than

10 inches living outside the region is different from that of the bats living in the

region. Which of the following is the correct test statistic?

z=.25-.30/sqr(0,3)(0.7)/80

A company that ships glass for a glass manufacturer claimed that its shipping boxes

are constructed so that no more than 8 percent of the boxes arrive with broken

glass. The glass manufacturer believed the actual percent is greater than 8 percent.

The manufacturer selected a random sample of boxes and recorded the proportion

of boxes that arrived with broken glass. The manufacturer tested the

hypotheses HH0:p=0.08 versus HHaa: p>0.08 at the significance level of αα=0.01. The test

yielded a p-value of 0.001. Assuming all conditions for inference were met, which of

the following is the correct conclusion?

The p-value is less than α, and the null hypothesis is rejected. There is

convincing evidence that the proportion of all boxes that contain broken glass is

greater than 0.08.

Past studies indicate that about 60 percent of the trees in a forested region are

classified as softwood. A botanist studying the region suspects that the proportion

might be greater than 0.60. The botanist obtained a random sample of trees from

the region and conducted a test of H0:p=0.6 versus Ha:p>0.6. The p-value of the

test was 0.015. Which of the following is a correct interpretation of the p-value?

If it is true that 60 percent of the trees in a forested region are classified as

softwood, 0.015 is the probability of obtaining a sample proportion as large as or

larger than the one obtained by the botanist.

A marketing agency selected a random sample of television viewers to test the

claim that the proportion of viewers who watch a particular show is less than 0.20 at

a level of significance of 0.05. The test yielded a p-value of 0.47. Assuming all

conditions for inference were met, which of the following is the correct conclusion?

At the level of significance of 0.05, the null hypothesis is not rejected. There is

not convincing evidence to suggest the true proportion of television viewers who

watch the show is less than 0.20.

10.Consider the results of a hypothesis test, which indicate there is not enough

evidence to reject the null hypothesis. Which of the following statements about

error is correct?

b. A Type II error could have been made, but not a Type I error.

Educators are testing a new program designed to help children improve their reading

skills. The null hypothesis of the test is that the program does not help children

improve their reading skills. For the educators, the more consequential error would

be that the program does not help children improve their reading skills but the test

indicated that it does help.

Which of the following should the researchers do to avoid the more consequential

error?

Decrease the significance level to decrease the probability of Type I error.

12.Machines at a bottling plant are set to fill bottles to 12 ounces. The quality control

officer at the plant periodically tests the machines to be sure that the bottles are

filled to an appropriate amount. The null hypothesis of the test is that the mean is at

least 12 ounces. The alternative hypothesis is that the mean is less than 12 ounces.

Which of the following describes a Type I error that could result from the test?

The test provides convincing evidence that the mean is less than 12 ounces, but

the actual mean is at least 12 ounces.

13.A biologist wants to compare the proportions of rainbow trout infected with whirling

disease (an illness of trout and salmon caused by a microscopic parasite) coming

from two separate watersheds. For each watershed, the biologist will collect a

random sample of trout and record the proportion infected in the sample. The

biologist intends to estimate the difference for all trout in the two watersheds.

Assuming all conditions for inference are met, which of the following is the most

appropriate method for the biologist to use to analyze the results?

d. A two-sample z-interval for a difference in population proportions

14.Which of the following is not a condition for constructing a confidence interval to

estimate the difference between two population proportions?

The data must come from populations with approximately normal distributions.

16.A study was conducted to investigate whether a new drug could significantly reduce

pain in people with arthritis. From a group of 500 people with arthritis, 250 were

randomly assigned to receive the drug (group 1) and the remaining people were

assigned a placebo (group 2). After one month of treatment, 225 people in group 1

reported pain relief and 150 people in group 2 reported pain relief. Let p^C represent

the combined (or pooled) sample proportion for the two samples. Have the

conditions for inference for testing the difference in population proportions been

met?

a. No. The people in the study were not selected at random.

b. No. The number of people in the study was too large compared with the size of

the population.

c. No. The normality of the sampling distribution cannot be assumed

because p^C times each sample size is not sufficiently large.

d. No. The normality of the sampling distribution cannot be assumed

because 1−p^C times each sample size is not sufficiently large.

e. Yes. All conditions for inference have been met.

Yes. All conditions for inference have been met.

17.Polydactyl cats are cats with extra toes. A researcher believes that the proportion of

the population of polydactyl cats in region A is greater than the proportion in region

B. Let ppAA represent the population proportion of polydactyl cats in region A, and

let ppBB represent the population proportion of polydactyl cats in region B. Which of

the following are the appropriate hypotheses to test the researchers belief?

b. Ho: pA − pB = 0; Ha: pA − pB > 0

Two locations of a fast-food restaurant, Location Q and Location W, were in a

certain town with a large number of residents. A nutritionist investigated whether

the proportion of orders that contained a salad was different at the two locations.

The nutritionist obtained a random sample of orders from the Location Q restaurant

and a random sample of orders from the Location W restaurant. Of the 215 Location

Q orders, 27 contained a salad; of the 175 Location W orders, 14 contained a salad.

Let pp̂

CC represent the combined sample proportion, and let nnQQ and nnWW represent the

respective sample sizes for Locations Q and W. Have the conditions for inference for

testing a difference in population proportions been met?

e. Yes, all conditions for making statistical inference have been met.

19.Maria has two routes, E and W, which she can take when commuting to work. Both

routes go through a railroad crossing, and sometimes she needs to stop at the

crossing to allow trains to pass. She claims that the proportion of times she needs

to stop when taking route E is different from the proportion of times she needs to

stop when taking route W. She conducted the following hypothesis test at the

significance level of αα = 0.10:

The p-value is greater than α, and the null hypothesis is not rejected. There is not

convincing evidence to support the claim that the proportion of times she needs

to stop at the crossing is different for the different routes.

20.A factory manager selected a random sample of parts produced on an old assembly

line and a random sample of parts produced on a new assembly line. The difference

between the sample proportion of defective parts made on the old assembly line

and the sample proportion of defective parts made on the new assembly line (old

minus new) was 0.006. Under the assumption that all conditions for inference were

met, a hypothesis test was conducted with the alternative hypothesis being the

proportion of defective parts made on the old assembly line is greater than that of

the new assembly line. The p-value of the test was 0.018.

If there is no difference in the proportions of all defective parts made on the two

assembly lines, the probability of observing a difference of at least 0.006 is

0.018.

Researchers at a medical center studied the amount of caƯeine, in milligrams (mg),

contained in a 16-ounce cup of coƯee made at one machine at the center’s

cafeteria. They selected a random sample of 40 16-ounce cups of coƯee made at

diƯerent times of the day during a one-month period. The mean and standard

deviation of the amount of caƯeine in the sample were 159.88 mg and 36.72 mg,

respectively. A graph of the sample data revealed a right skew with one outlier. The

researchers will construct a confidence interval to estimate the amount of caƯeine

for all 16-ounce cups made at the machine.

Which of the following conditions is not needed for the inference?

The graph of the sample data is symmetric with no outliers.

A random sample of 10 employees of a company was selected to estimate the

mean one-way commute time for all employees at the company. The mean and

standard deviation of the sample were 38 minutes and 6 minutes, respectively.

Assuming all conditions for inference are met, which of the following is the margin

of error, in minutes, for a 95 percent confidence interval for the population mean

one-way commute time?

2.262(6/√10)

A university researcher wants to estimate the mean number of novels that seniors

read during their time in college. An exit survey was conducted with a random

sample of 9 seniors. The sample mean was 7 novels with standard deviation 2.29

novels. Assuming that all conditions for conducting inference have been met, which

of the following is a 95 percent confidence interval for the population mean number

of novels read by all seniors?

7 ± 2.262(2.29/√9)

Which of the following correctly compares the t-distribution and z-distribution?

The density curve of the t-distribution is more spread out than the density curve

of the z-distribution, especially for small sample sizes.

Animal scientists studied foraging behavior of the scrub lizard, found in central

Florida. Foraging is the process of searching for food. To study such behavior, the

scientists recorded the number of head movements per minute for a sample of 63

lizards. A 95 percent confidence interval constructed from the sample is given

as 2.7±0.62 head movements per minute.

Based on the interval, is a claim of 3 head movements per minute plausible?

The claim is plausible because 3 head movements per minute is contained

within the interval.

An environmental agency frequently samples the water in a region to ensure that

the levels of a certain contaminant do not exceed 30 parts per billion (ppb). From 12

randomly selected samples of the water, the agency constructed the 99 percent

confidence interval (22.5, 28.7).

Assuming all conditions for inference are met, which of the following is a correct

interpretation of the interval?

We are 99 percent confident that the mean level of the contaminant in all the

water in the region is between 22.5 ppb and 28.7 ppb.

A business analyst is investigating whether the mean amount of purchases made by

customers at an online department store is greater than $100. The analyst obtained

a random sample of 56 orders and calculated a sample mean of $102.30 and a

sample standard deviation of $5.30.

a. A one-sample t-test for a population mean

A fast-food restaurant claims that a small order of French fries contains 120

calories. A nutritionist is concerned that the true average calorie count is higher

than that. The nutritionist randomly selects 35 small orders of French fries and

determines their calories. The resulting sample mean is 155.6 calories, and the p-

value for the hypothesis test is 0.00093.

Which of the following is a correct interpretation of the p-value?

If the population mean is 120 calories, the p-value of 0.00093 is the probability of observing a sample mean of 155.6 calories or more.

A century ago, the average height of adult women in the United States was 63

inches. Researchers believe that the average might be greater today. A random

sample of 40 adult women was selected from the population. The sample had mean

64.2 inches and standard deviation 2.9 inches. Assuming all conditions for

inference are met, the researchers will perform an appropriate hypothesis test to

investigate their belief.

Which of the following is the correct test statistic for the hypothesis test?

. t = (64.2 - 63) / (2.9/√40)

10.Most dermatologists recommend that the ideal shower lasts approximately 10

minutes. A researcher suspects that the average shower length of high school

students is greater than 10 minutes. To test the belief, the researcher surveyed 125

randomly selected high school students and found that their average shower length

was 14.7 minutes. With all conditions for inference met, a hypothesis test was

conducted at the significance level of α=0.05, and the test produced a p-value of

0.0000. Which of the following is an appropriate conclusion?

The researcher has statistical evidence to conclude that the population mean

shower length for high school students is greater than 10 minutes.

A national consumer agency selected independent random samples of 45 owners

of newer cars (less than five years old) and 40 owners of older cars (more than five

years old) to estimate the difference in mean dollar cost of yearly routine

maintenance, such as oil changes, tire rotations, filters, and wiper blades. The

agency found the mean dollar cost per year for newer cars was $195 with a standard

deviation of $46. For older cars, the mean was $286 with a standard deviation of

$58.

Which of the following represents the 95 percent confidence interval to estimate

the difference (newer minus older) in the mean dollar cost of routine maintenance

between newer and older cars?

(195 − 286) ± 1.992sqr46/45 + 58/40

Researchers investigated whether there is a difference between two headache

medications, R and S. Researchers measured the mean times required to obtain

relief from a headache for patients taking one of the medications. From a random

sample of 75 people with chronic headaches, 38 were randomly assigned to

medication R and the remaining 37 were assigned to medication S. The time, in

minutes, until each person experienced relief from a headache was recorded. The

sample mean times were calculated for each medication.

Have the conditions been met for inference with a confidence interval for the

difference in population means?

a. Yes, all conditions have been met.

A researcher in sports equipment is investigating the design of racing swimsuits for

women. The researcher selected a sample of 40 women swimmers from high

school swim teams in the state and randomly assigned each swimmer to one of two

groups: suit A or suit B. The women will wear the assigned suits for a certain race,

and the mean swim times for each group will be recorded. The difference in the

sample mean swim times will be calculated.

Which of the following is the appropriate inference procedure for analyzing the

results?

e. A matched-pairs t-interval for a mean difference

Alicia would like to know if there is a difference in the average price between two

brands of shoes. She selected and analyzed a random sample of 40 different types

of Brand A shoes and 33 different types of Brand B shoes. Alicia observes that the

boxplot of the sample of Brand A shoe prices shows two outliers. Alicia wants to

construct a confidence interval to estimate the difference in population means.

Is the sampling distribution of the difference in sample means approximately

normal?

No, because the distribution of Brand A shoes has outliers.

A biologist studied the frequency of croaks for frogs from two different regions.

From a random sample of 32 frogs located in the northern region, the mean number

of croaks per hour was 21.3, and from a random sample of 38 frogs located in the

southern region, the mean number of croaks per hour was 28.9. To estimate the

difference in the mean number of croaks (southern minus northern), a 95 percent

confidence interval was constructed from the samples. The interval was reported

as (7.1,8.1).

Which of the following claims is supported by the interval?

The southern frogs are likely to have a greater mean number of croaks per hour

than the northern frogs.

To test the durability of cell phone screens, phones are dropped from a height of 1

meter until they break. A random sample of 40 phones was selected from each of

two manufacturers. The phones in the samples were dropped until the screens

broke. The difference in the mean number of drops was recorded and used to

construct the 90 percent confidence interval (0.46,1.82) to estimate the population

difference in means.

Consider the sampling procedure taking place repeatedly. Each time samples are

selected, the phones are dropped and the statistics are used to construct a 90

percent confidence interval for the difference in means. Which of the following

statements is a correct interpretation of the intervals?

Approximately 90 percent of the intervals constructed will capture the

difference in population means.

A soda manufacturer claims that its Cherry Fizz soda has more carbonation than a

competitor’s Cherry Eclipse soda. Bottles of both types of soda are opened,

covered with a balloon, and then shaken. The diameter of each balloon is then

measured. The mean balloon diameters are 2.3 inches for the Cherry Fizz soda and

2.1 inches for the Cherry Eclipse soda. A 90 percent confidence interval to estimate

the difference in mean diameters, in inches, is (−0.8,1.2). Which of the following

claims is supported by the interval?

Because the interval contains 0, it is possible that there is no difference in mean

carbonation levels.

A study was conducted to investigate whether the mean price of a dozen eggs was

different for two different grocery stores, Store A and Store B, in a large city. A carton

of one dozen eggs from each store was randomly selected for each of 35 weeks, for

a total sample size of 35 cartons from each store. The mean price of the 35 cartons

was recorded for each store. The difference in the mean carton price for the stores

will be calculated.

Which of the following is the appropriate test for the study?

A two-sample t-test for a difference between population means

9. Two siblings, Alice and Sean, are both convinced that they are faster than the other

at solving a puzzle cube. They recorded the length of time it took them to solve the

cube 18 times each during a one-month period. Then each calculated the mean

amount of time and standard deviation, in minutes, for their times. Let μ஺ equal the

mean time it took Alice to solve the puzzle cube and μௌ

equal the mean time it took

Sean. Which of the following are the appropriate null and alternative hypotheses to

test for a difference in time for the siblings to solve the cube?

Ho: μA − μS= 0; Ha: μA − μS≠ 0

A two-sample t-test for a difference in means was conducted to investigate whether

defensive players on a football team can bench-press more weight, on average,

than offensive players. The conditions for inference were met, and the test

produced a test statistic of t=1.083 and a p-value of 0.15.

Based on the p-value and a significance level of α=0.05, which of the following is the

correct conclusion?

Fail to reject the null hypothesis because 0.15>0.05. There is not convincing

evidence that defensive players can bench-press more weight, on average, than

offensive players.