AP Statistics chapter 10 review

You want to compute a 96% confidence interval for a population mean. Assume that the population standard deviation is known to be 10 and the sample size is 50. The critical value to be used in this calculation is:

A) 1.960

B) 1.645

C) 1.757

D) 2.054

E) None of the above

D) 2.054

You have measured the systolic blood pressure of a random sample of 25 employees. A 95% confidence interval for the mean systolic blood pressure for the employees is 122,138. Which of the following statements gives a valid interpretation of this interval?

A) Ninety-five percent of the sample of employees have a systolic blood pressure between 122 and 138

B) Ninety-five percent of the population of employees have a systolic blood pressure between 122 and 138

C) If the procedure were repeated many times, 95% of the resulting confidence intervals would contain the population mean systolic blood pressure

D) The probability that the population mean blood pressure is between 122 and 138 is 0.95

E) None of the above

C) If the procedure were repeated many times, 95% of the resulting confidence intervals would contain the population mean systolic blood pressure

An analyst, using a random sample of n=500 families, obtained a 90% confidence interval for mean monthly family income for a large population: ($600,$800). If the analyst had used a 99% confidence level instead, the confidence interval would be:

A) Narrower and would involve a larger risk of being incorrect

B) Wider and would involve a smaller risk of being incorrect

C) Narrower and would involve a smaller risk of being incorrect

D) Wider and would involve a larger risk of being incorrect

E) Wider but it cannot be determined whether the risk of being incorrect would be larger or smaller

B) Wider and would involve a smaller risk of being incorrect

In an opinion poll, 25% of a random sample of 200 people said that they were strongly opposed to having a state lottery. The standard error of the sample proportion is approximately:

A) 0.03

B) 0.25

C) 0.0094

D) 6.12

E) 0.06

F) None of the above

A) 0.03

In preparing to use a t procedure, suppose we were not sure if the population was Normal. In which of the following circumstances would we not be safe using a t procedure?

A) A stemplot of the data is roughly bell-shaped

B) A histogram of the data shows moderate skewness

C) A stemplot of the data that has a large outlier

D) The sample standard deviation is large

E) The t procedure are robust, so it is always safe

C) A stemplot of the data that has a large outlier

Some scientists believe that a new drug would benefit about half of all people with a certain blood disorder. To estimate the proportion of patients who would benefit from taking the drug, scientists will administer it to a random sample of patients who have the blood disorder. What sample size is needed so that the 95% confidence interval will have a width of 0.06?

A) 748

B) 1068

C) 1503

D) 2056

E) 2401

B) 1068

In a poll, (a) some people refused to answer questions, (b) people without telephones could not be in the sample, and (c) some people never answered the phone in several calls. Which of these sources is included in the ±2% margin of error announced for the poll?

A) only source (a)

B) only source (b)

C) only source (c)

D) all three are sources of error

E) none of these are sources of error

E) none of these are sources of error

Researchers are studying yield of a crop in two locations. The researchers are going to compare two independent 90% confidence intervals for the mean yield in each location. The probability that at least one of the constructed intervals will cover the true mean yield at its location is

A) 0.81

B) 0.19

C) 0.99

D) 0.95

E) none of these

C) 0.99

Suppose that the population of the scores of all high school seniors who took the Math

SAT (SAT-M) test this year follows a normal distribution with mean μ and standard

deviation s = 100. You read a report that says, "On the basis of a simple random

sample of 100 high school seniors that took the SAT-M test this year, a confidence

interval for μ is 512.00 ± 25.76." The confidence level for this interval is

A) 90%.

B) 95%.

C) 96%.

D) 99%.

E) none of these.

D

A 90% confidence interval for the mean μ of a population is computed from a random

sample and is found to be 9 ± 3. Which of the following could be the 95% confidence

interval based on the same data?

A) 9 ± 1.96.

B) 9 ± 2.

C) 9 ± 3.

D) 9 ± 4.

E) Without knowing the sample size, any of the above answers could be the 95%

confidence interval.

D) 9 ± 4

You want to compute a 90% confidence interval for the mean of a population with unknown

population standard deviation. The sample size is 30. The value of t* you would use for this

interval is

(A) 1.960.

(B) 1.645.

(C) 1.699.

(D) 0.900.

(E) 1.311.

(F) none of the above.

C) 1.699

A polling organization announces that the proportion of American voters who favor

congressional term limits is 64%, with a 95% confidence margin of error of 3%. This means:

(A)If the poll were conducted again in the same way, there is a 95% chance that the fraction

of voters favoring term limits in the second poll would be between 61% and 67%.

(B) There is a 95% probability that the true percent of voters favoring term limits is between

61% and 67%.

(C) If the poll were conducted again the same way, there is a 95% probability that the percent

of voters favoring term limits in the second poll would be within 3% of the percent

favoring term limits in the first poll.

(D)Among 95% of the voters, between 61% and 67% favor term limits.

(E) none of the above.

E) none of the above

A radio talk show host with a large audience is interested in the proportion p of adults in his

listening area who think the drinking age should be lowered to eighteen. To find this out he

poses the following question to his listeners. "Do you think that the drinking age should be

reduced to eighteen in light of the fact that eighteen-year-olds are eligible for military

service?" He asks listeners to phone in and vote "Yes" if they agree the drinking age should

be lowered and "No" if not. Of the 100 people who phoned in, 70 answered "Yes." Which

of the following conditions for inference about a proportion using a confidence interval are

violated?

(A)The data are an SRS from the population of interest.

(B) The population is at least 10 times as large as the sample.

(C) n is so large that both the count of successes np and the count of failures n(1 - p) are 10

or more.

(D)There appear to be no violations.

(E) More than one condition is violated.

A) the data are an SRS from the population of interest

To assess the accuracy of a laboratory scale, a standard weight that is known to weigh 1 gram is repeatedly weighed a total of n times and the mean of the weighings is computed.

Suppose the scale readings are Normally distributed with unknown mean and standard

deviation = 0.01 g. How large should n be so that a 95% confidence interval for has a margin of error of ± 0.0001?

(A)100

(B) 196

(C) 27,061

(D) 10,000

(E) 38,416

E) 38,416

A 95% confidence interval for the mean reading achievement score for a population of third-grade students is (44.2, 54.2). Suppose you compute a 99% confidence interval using the same information. Which of the following statements is correct?

(A) The intervals have the same width.

(B) The 99% interval is shorter.

(C) The 99% interval is longer.

(D) The answer can't be determined from the information given.

(E) none of the above.

C) the 99% interval is longer

A random sample of 900 individuals has been selected from a large population. It was found that 180 are regular users of vitamins. Thus, the proportion of the regular users of vitamins in the population is estimated to be 0.20. The standard error of this estimate is approximately

(A)0.1600

(B) 0.0002

(C) 0.4000

(D)0.0133

(E) 0.0267

D) 0.0133

The weights of 9 men have mean = 175 pounds and standard deviation s = 15 pounds. What is the standard error of the mean?

(A)58.3

(B) 19.4

(C) 5.0

(D) 1.7

(E) none of the above

C) 5.0

An agricultural researcher plants 25 plots with a new variety of corn. The average yield for these plots is = 150 bushels per acre. Assume that the yield per acre for the new

variety of corn follows a normal distribution with unknown mean μ and standard

deviation s = 10 bushels. A 90% confidence interval for μ is

(A) 150 ± 2.00.

(B) 150 ± 3.29.

(C) 150 ± 3.92.

(D) 150 ± 16.45.

(E) 150 ± 32.90.

(B) 150 ± 3.29

A private college has a total of 350 students. The Math SAT (SAT-M) score is required

for admission. The mean SAT-M score of all 350 students is 630, and the standard

deviation of SAT-M scores for all 350 students is 40. The formula for a 95% confidence

interval yields the interval 630 ± 5.52. We may conclude that

A) 95% of all student Math SAT scores will be between 624.48 and 635.52.

B) if we repeated this procedure many, many times, only 5% of the 95% confidence

intervals would fail to include the mean SAT-M score of the population of all

students at the college.

C) 95% of the time, the population mean will be between 624.48 and 635.52.

D) the interval is incorrect; it is much too small.

E) none of the above is true.

E) none of the above is true

Suppose that the population of the scores of all high school seniors who took the Math

SAT (SAT-M) test this year follows a normal distribution with mean μ and standard

deviation s = 100. We take an SRS of n = 100 high school seniors that took the SAT-M

test this year. The sample mean was = 512. A 90% confidence interval for μ is

(A) (486.24, 537.76)

(B) (491.46, 532.54)

(C) (492.40, 531.60)

(D) (495.55, 528.45)

(E) none of these.

(D) (495.55, 528.45)

A 95% confidence interval for the mean μ of a population is computed from a random

sample and found to be 10 ± 4. We may conclude that

A) there is a 95% probability that μ is between 6 and 14.

B) 95% of values sampled are between 6 and 14.

C) if we took many, many additional random samples and from each computed a 95%

confidence interval for μ, approximately 95% of these intervals would contain μ.

D) there is a 95% probability that the true mean is 10 and a 95% chance that the true

margin of error is 4.

E) all of the above are true.

C) if we took many, many additional random samples and from each computed a 95%

confidence interval for μ, approximately 95% of these intervals would contain μ.

Suppose that the population of the scores of all high school seniors who took the SAT Math

test this year follows a Normal distribution with mean and standard deviation = 100.

You read a report that says, "on the basis of a simple random sample of 100 high school seniors that took the SAT-M test this year, a confidence interval for is 512.00 ± 44.17."

The confidence level for this interval is

(A) 90%. (E) over 99.9%

(B) 95%.

(C) 99%

(D) 99.5%

E) over 99.9%

The government claims that students earn an average of $4500 during their summer break

from studies. A random sample of students gave a sample average of $3975, and a 95%

confidence interval was found to be $3525 < μ < $4425. This interval is interpreted to mean

that

(A) there is a 95% probability of confidence that you will get this question right.

(B) because our specific confidence interval does not contain the value $4500 there is a 95%

probability that the true average summer earnings is not $4500.

(C) if we were to repeat our survey many times, then about 95% of all the confidence

intervals will contain the value $4500.

(D) if we repeat our survey many times, then about 95% of our confidence intervals will

contain the true value of the average earnings of students.

(E)there is a 95% probability that the true average earnings are between $3525 and $4425

for all students.

(D) if we repeat our survey many times, then about 95% of our confidence intervals will

contain the true value of the average earnings of students.

Many television viewers express doubts about the validity of certain commercials. In an attempt to answer their critics, the Timex Corporation wishes to estimate the proportion of

consumers who believe what is shown in Timex television commercials. Let p represent the true proportion of consumers who believe what is shown in Timex television commercials. If Timex has no prior information regarding the true value of p, how many consumers should be included in their sample so that they will be 85% confident that their estimate is within 0.03 of the true value of p?

(A)400

(B) 12

(C) 576

(D)384

(E) 512

C) 576

A polling organization announces that the proportion of American voters who favor

congressional term limits is 64%, with a 95% confidence margin of error of 3%. If the

opinion poll had announced the margin of error for 80% confidence rather than 95%

confidence, this margin of error would be

(A) 3%, because the same sample is used.

(B) less than 3%, because we require less confidence.

(C) less than 3%, because the sample size is smaller.

(D) greater than 3%, because we require less confidence.

(E) greater than 3%, because the sample size is smaller.

(B) less than 3%, because we require less confidence.

Suppose we want a 90% confidence interval for the average amount spent on books by freshmen in their first year at a major university. The interval is to have a margin of error of $2, and the amount spent has a Normal distribution with a standard deviation = $30. The

number of observations required is closest to

(A)25.

(B) 30.

(C) 608.

(D) 609.

(E) 865.

D) 608

The college newspaper of a large Midwestern university periodically conducts a survey of students on campus to determine the attitude on campus concerning issues of interest. Pictures of the students interviewed along with quotes of their responses are printed in the paper. Students are interviewed by a reporter "roaming" the campus selecting students to

interview "haphazardly." On a particular day the reporter interviews five students and asks them if they feel there is adequate student parking on campus. Four of the students say, "no." Which of the following conditions for inference about a proportion using a confidence interval are violated in this example?

(A)The data are an SRS from the population of interest.

(B) The population is at least ten times as large as the sample.

(C) 10 and .

(D)We are interested in inference about a proportion.

(E) More than one condition is violated.

E) more than one condition is violated

A 95% confidence interval for p, the proportion of Canadian beer drinkers who prefer Lion

Red, was found to be (0.236, 0.282). Which of the following is correct?

(A)About 95% of beer drinkers have between a 23.6% and a 28.2% chance of drinking Lion

Red.

(B) There is a 95% probability that the sample proportion lies between 0.236 and 0.282.

(C) If a second sample was taken, there is a 95% chance that its confidence interval would

contain 0.25.

(D)This confidence interval indicates that more than 25% of Canadian beer drinkers prefer

Lion Red.

(E) None of these.

E) none of these

What is the critical value t* that satisfies the condition that the t distribution with 8 degrees of

freedom has probability 0.10 to the right of t*?

(A)1.397

(B) 1.282

(C) 2.89

(D) 0.90

(E) none of the above

A) 1.397