1Final Exam Review

AP Statistics Final Exam Review 

I. Multiple Choice 

1. You have sampled 25 students to find the mean SAT scores at Morris Knolls High School. 

A 95% confidence interval for the mean SAT score is 900 to 1100. Which of the following 

statements gives a valid interpretation of this interval 

A) 95% of the 25 students have a mean score between 900 and 1100 

B) 95% of the population of all students at Morris Knolls have a score between 900 and 

1100 

C) If this procedure were repeated many times, 95% of the resulting confidence intervals 

would contain the true mean SAT score at Morris Knolls 

D) If this procedure were repeated many times, 95% of the sample means would be 

between 900 and 1100 

E) If 100 samples were taken and a 95% confidence interval was computed, 5 of them 

would be in the interval from 900 to 1100 

2. According to a poll, approximately 30% of Americans spent over $750 on holiday presents 

in 1998. Suppose you took a random sample of 85 shoppers and found that 23 spent over 

$750 on holiday presents in 1999. What test statistic would you use to conduct a hypothesis 

test to see if the percentage of people spending more than $750 on holiday presents has 

decreased 

A) 

23 

85 

!.3 

(.3)(.7) 

85 

B) 

.3 

(.3)(.7) 

85 

C) z - 

pˆ 

n 

D) 

23 

85 

! 

( 

23 

85 

)( 

85 

.3 

62 

85 

) 

E) 

23 

85 

( 23 62 

85)( 

85) 

85 

3. A sampling distribution (n=20) of the number of penalties served last season by members of 

the Hitemhard hockey team has a mean of 2,000 with a standard error of 53. What is the 

probability of obtaining a sample mean that is less than 145 

A) 0.1551 

B) 0 

C) 1.557 

D) 0.1557 

E) 0.005 

1final exam review.doc p. 1

4. A large sample hypothesis test with σ known, a null hypothesis of µ = 15, and an alternative 

hypothesis of µ ≠ 15 results in the test statistic value of z = 1.37. Assuming σ is known, the 

corresponding P-value is approximately 

A) 0.0853 B) 0.1707 C) 0.4147 D) 0.8293 E) 0.9147 

5. The level of significance is always 

A) the maximum allowable probability of Type II error 

B) the maximum allowable probability of Type I error 

C) the same as the confidence 

D) the same as the P-value 

E) 1 – P(type II error) 

6. Which of the following is (are) true 

I. If the sample size is constant, then reducing the probability of Type I error will reduce 

the probability of Type II error 

II. Increased power can be achieved by reducing the type II error 

III. If the P-value of a test is 0.015, the probability that the null hypothesis is true is 0.015 

A) I only 

B) II only 

C) I and III only 

D) II and III only 

E) I, II, and III 

7. At a certain high school a simple random sample was taken asking fifty-two 11 th and 12 th 

graders their political affiliation. The following two-way table was established. If a χ 2 test 

of independence were performed on these data, what would be the corresponding degrees of 

freedom 

11 th Grade 12th Grade 

Republican 11 5 

Democrat 10 15 

Independent 5 6 

A) 1 B) 2 C) 3 D) 6 E) 25 


8. Failing to reject a null hypothesis that is false can be characterized as 

A) a Type I error 

B) a Type II error 

C) both a Type I and a Type II error 

D) a standard error of the mean 

E) no error 

9. If a 95% confidence interval is given by (86.52, 89.48), which of the following could be a 

99% confidence interval for the same data 

I. (86.98, 89.02) 

II. (86.37, 89.63) 

III. (87, 89) 

A) I only 

B) II only 

C) III only 

D) I and III 

E) II and III 

10. In constructing a confidence interval based on a large sample to estimate the mean µ of a 

population with known standard deviation σ, which of the following does NOT affect the 

width of the confidence interval 

A) the sample mean 

B) the population standard deviation 

C) the confidence level 

D) the sample size 

E) the population mean 

11. Which of the following accurately describes the power of a statistical test of a hypothesis 

A) It is equal to the P-value 

B) It is equal to 1 – (P-value) 

C) It is equal to α, the significance level 

D) It is the probability that a test using a fixed value of α will reject H0 when a particular 

alternative value of the parameter is true 

E) It is equal to β 


12. An inspector inspects large truckloads of potatoes to determine the proportion p in the 

shipment with major defects prior to using the potatoes to make potato chips. Unless there is 

clear evidence that this proportion is less than 0.10, she will reject the shipment. To reach a 

decision she will test the hypotheses 

H 0 : p = 0.10, H a : p < 0.10 

using the large sample test for a population proportion. To do so, she selects an SRS of fifty 

potatoes from the over 2000 potatoes on the truck. Suppose that only two of the potatoes 

sampled are found to have major defects. 

The P-value of her test is 

A) 0.4207. B) 0.0786. C) 0.0154. D) less than 0.0002. 

13. A tire manufacturer claims that it has developed a new all-season radial tire for passenger 

cars (excluding SUVs) which has a shorter skid distance than the known mean skid distance, 

140 feet, for all tires currently available. A consumer group wishes to test this claim. If µ 

represents the true mean skid distance for this new tire, which of the following states the null 

hypothesis and alternative hypothesis that the consumer group should test 

A) H 0 : µ < 140 ft. H a : µ ≥ 140 ft. 

B) H 0 : µ ≤ 140 ft. H a : µ > 140 ft. 

C) H 0 : µ = 140 ft. H a : µ < 140 ft. 

D) H 0 : µ = 140 ft. H a : µ ≤ 140 ft. 

E) H 0 : µ = 140 ft. H a : µ ≠ 140 ft. 

14. A building inspector believes that the percentage of new construction with serious code 

violations may be even greater than the previously claimed 7%/ she conducts a hypotesis 

test on 200 new homes and finds 23 with serious code violations. Is this strong evidence 

against the .07 claim 

A) Yes, because the p-value is .0062 

B) Yes, because the p-value is 2.5 

C) No, because the p-value is .0062 

D) No, because the p-value is over 2.0 

E) No, because the p-value is .045 


15. A telephone survey of 1000 adult Americans reveals the following data concerning the 

President’s tax cut plan: 

Support Oppose Undecided 

Male 300 180 90 

Female 210 190 30 

Suppose a study is conducted to test the association between gender and position on the tax 

cut plan. What is the expected number in the cell representing females who support the tax 

cut plan 

A) 210 

B) 215 

C) 219.3 

D) 240.3 

E) Not enough information given 

16. A historian believes that the average height of soldiers in World War II was greater than that 

in World War I. She examines a random sample of records of 100 men in each war and 

notes standard deviations of 2.5 inches for WWI and 2.3 inches for WWII. If the average 

height from the sample of World War II soldiers is 1 inch greater than that from World War 

I soldiers, what conclusion is justified from a two-sample hypothesis where. 

H : µ µ and H µ < µ 

0 1 

= 

2 

a 

: 

1 

2 

A) The observed difference in average height is significant 

B) The observed difference in height is not significant 

C) A conclusion os not possible without knowing the mean height in each sample 

D) A conclusion is not possiblewithout knowing both the sample means and the two 

original population sizes 

E) A two-sample hypothesis test should not be used in this sample 

17. Two independent random samples of size n 1 = 45 and n 2 = 38, with respective standard 

deviations σ 1 = 2.3 and σ 2 = 1.8, are drawn from two normally distributed populations. 

Which of the following represents an estimate of the standard deviation of the sampling 

distribution corresponding to x 

1 

! x2 

 

A) 0.25 B) 0.31 C) 0.45 D) 0.50 E) 2.05 


18. A researcher wishes to use a 95% confidence interval to estimate the proportion of 

Americans who have visited an entertainment theme park near Orlando within the last five 

years. The searcher wishes to choose a size that will insure a margin of error not to exceed 

0.05. Which of the following is the smallest size that meets these criteria 

A) 40 B) 200 C) 400 D) 600 E) 800 

19. A health fitness group wishes to estimate the mean amount of time (in hours) that members 

of a fitness center spend each week exercising at the center. They want to estimate the mean 

within a margin of error of 0.5 hours with a 95% level of confidence. Previous data suggests 

that σ = 2.2. Which of the following is the smallest sample size that meets these criteria 

A) 60 B) 75 C) 90 D) 180 E) 190 

20. Data was collected to test whether there is a difference between the mean heights of women 

born in two different countries. It is assumed that the heights of women in each of these 

countries are normally distributed. Also, there is no reason to believe that population 

variances of the population of heights of women from the two different countries are equal. 

The data collected indicate the following: 

n 1 = 130 x 

1 

= 63. 8 s 1 = 2.3 

n 2 = 190 x 

2 

= 62. 4 s 2 = 2.7 

Which of the following represents an estimate of the standard deviation of the sampling 

distribution corresponding to x 

1 

! x2 

 

A) 0.04 B) 0.29 C) 2.24 D) 2.50 E) 3.16 

21. In a sample survey taken of 450 residents of a given community, 180 of them indicated that 

they shop at the local mall at least once per month. Construct a 95% confidence interval to 

estimate the true percentage of the residents who shop monthly at the local mall. 

A) (0.355, 0.445) 

B) (0.366, 0.434) 

C) (0.377, 0.423) 

D) (0.380, 0.420) 

E) It cannot be determined from the information given 

22. 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 to 

construct this interval is: 

A) 0.90 B) 1.311 C) 1.645 D) 1.699 E) 1.96 


23. A researcher wishes to test the following hypothesis: 

H 0 : µ = 100 

H a : µ < 100 

If the population mean is actually 95, but the researcher concludes that the mean is 100, 

what type of error has occurred 

A) Type I error 

B) Type II error 

C) Standard error of the mean 

D) No error has occurred 

E) The data do not provide enough information to determine the type of error 

24. A consumer group believes that boxes of Sugar Toasties Cereal contain, on average, less 

than the 15 ounces of cereal as advertised. They randomly sample 36 boxes of this cereal 

and find the mean x = 14. 9 and standard deviation s = 0.43. Assume that the weights are 

normally distributed and that α = 0.05. In testing the consumer group’s claim, what is the P- 

value for this hypothesis test 

A) –0.6511 

B) 0.0001 

C) 0.0500 

D) 0.0859 

E) 0.2547 

25. A standard 6-sided die was rolled 24 times with the following results: 

Number of dots 1 2 3 4 5 6 

Frequency 2 8 2 1 3 8 

A goodness-of-fit χ 2 test is to be used to test the null hypothesis that the die is fair. At a 

significance level of α = 0.01, the value of the χ 2 statistic and the statistical conclusion are: 

A) χ 2 = 12.5; fail to reject the null hypothesis 

B) χ 2 = 12.5; reject the null hypothesis 

C) χ 2 = 25.0; fail to reject the null hypothesis 

D) χ 2 = 25.0; reject the null hypothesis 

E) χ 2 = 75.5; reject the null hypothesis 


II. 

Free Response. Show all work. Clearly indicate the methods you use. If you use 

your calculator, clearly indicate the test, inputs, settings, and outputs. For 

hypothesis tests, clearly give H 0 and H a , in both words and symbols (where 

applicable). 

1. All current-carrying wires produce electromagnetic (EM) radiation, including the 

electrical wiring running into, through, and out of our homes. High frequency EM 

radiation is thought to be a cause of cancer; the lower frequencies associated with 

household current are generally assumed to be harmless. To investigate this 

possibility, researchers visited the addresses of children in the Denver area who had 

died of some form of cancer (leukemia, lymphoma, or some other type) and 

classified the wiring configuration outside the building as either a high-current 

configuration (HCC) or a low-current configuration (LCC). Here are some of the 

results of the study. 

Leukemia Lymphoma Other cancers 

HCC 52 10 17 

LCC 84 21 31 

The Minitab output for the above table is given below. The output includes the cell counts, 

the expected cell counts, and the chi-square statistic. Expected counts are printed below 

observed counts. 

Leukemia Lymphoma Other cancers Total 

HCC 52 10 17 79 

49.97 11.39 17.64 

LCC 84 21 31 136 

86.03 19.61 30.36 

Total 136 31 48 215 

ChiSq = 0.082 + 0.170 + 0.023 + 0.048 + 0.099 + 0.013 = 0.435 

a. The appropriate degrees of freedom for the chi-square statistic is 

b. The P-value for the chi-square statistic is between what two values 

c. The cell that contributes most to the chi-square statistic is 

d. What may we conclude 


2. A Television Marketing Group (TMG) claims that at least three out of every four 

Americans believe that reality-based television shows are untruthful. They tested 

their claim by using data from a recent Gallup poll which indicated that in a sample 

of 1,015 Americans, 812 thought the shows were either somewhat or totally 

untruthful. 

a. Test the claim of the TMG using a significance level of 0.01. State 

clearly your assumptions and what test of hypothesis you are using. 

Find the appropriate P-value and interpret your results within the 

context of the problem. 

b. Construct a 95% confidence interval to estimate the true proportion of 

Americans who think these shows are essentially untruthful. 


3. In 1908 W.S. Gosset wrote a paper titled, “The Probable Error of a Mean.” In the 

paper Gossett reported on the corn yield using two different kinds of seeds. The first 

seed was the usual seed used by farmers in England at the time. The second seed 

type was kiln-dried. Each type of seed was planted in adjacent plots, accounting for 

11 pairs of “split” plots. The data are given below. The numbers are in pounds per 

acre. 

Plot # 

Yield for 

Regular Seed 

Yield for Kiln- 

Dried Seed 

1 1903 2009 

2 1935 1915 

3 1910 2011 

4 2496 2463 

5 2108 2180 

6 1961 1925 

7 2060 2122 

8 1444 1482 

9 1612 1542 

10 1316 1443 

11 1511 1535 

The following computer outputs show the descriptive statistics of the two variables and a 

regression output which resulted from fitting a least squares regression line using yield from 

“regular” seed to predict yield from “kiln-dried” seed. 

Variable N Mean Median TrMean StDev SE Mean 

Regular 11 1841 1910 1827 343 103 

Kiln-Dri 11 1875 1925 1858 333 100 

Variable Minimum Maximum Q1 Q3 

Regular 1316 2496 1511 2060 

Kiln-Dri 1443 2463 1535 2122 

Predictor Coef SE Coef T P 

Constant 120.4 116.7 1.03 0.329 

Regular 0.95293 0.06241 15.27 0.000 

S = 67.6459 R-Sq = 96.3% R-Sq(adj) = 95.9% 


Below are a residual plot and a normal quantile plot of the residuals resulting from the regression. 

100 

Residuals Versus Regular 

(response is Kiln-Dri) 

99 

Normal Probability Plot of the Residuals 

(response is Kiln-Dri) 

50 

95 

90 

Residual 

0 

80 

Percent 

70 

60 

50 

40 

-50 

30 

20 

10 

-100 

5 

1200 

1400 

1600 

1800 2000 

Regular 

2200 

2400 

2600 

1 

-150 

-100 

-50 

0 

Residual 

50 

100 

150 

a. Use side-by-side box plots to compare the corn yield for the two groups. 

Write a few sentences commenting on your display. 

b. Can yield of “regular seed” be used to predict the yield of “kiln dried 

seed” Give statistical justification to support your response. 


4. An educational group claims that teaching fraction concepts using math 

manipulatives results in higher student achievement and understanding of fractions 

than teaching fractions without the use of any math manipulatives. A teacher in a 

middle school taught a unit on fractions to two sixth grade classes, one using math 

manipulatives and the other without the use of any manipulatives. The table below 

shows the performance of these two classes on a unit test on fractions. 

With Manipulatives Without Manipulatives 

85 78 

75 84 

83 81 

87 78 

80 76 

79 83 

88 79 

94 75 

87 85 

82 81 

Test the claim that students who use manipulatives show higher achievement on a test of 

fractions. Give appropriate statistical evidence to support your answer. 


5. In a nationwide random sample of 550 high school boys and 430 high school girls, 

all of which have been caught cheating by their teachers at some time, 253 boys and 

172 girls admitted to cheating on an exam. Is this sufficient evidence to say that 

boys are more likely to admit to cheating than girls Provide appropriate statistical 

evidence. 


6. A medical research team is conducting a study to determine whether there is a 

relationship between aerobic walking and cholesterol levels. A random sample of 

315 subjects is selected and represented in the table below. Test the claim that 

aerobic walking and cholesterol levels are related. Include appropriate statistical 

evidence to support your findings. 

Low Average Elevated 

Walkers 51 86 31 

Non-Walkers 23 94 30 

7. A new cell phone company offers a selection of five colors in their designer 

corporate package. The company claims that the 5 colors are equally distributed 

among all phones. Goodinvest.com orders 10 corporate packages of 10 phones each 

and randomly received 18 red, 17 blue, 20 green, 24 purple, and 21 orange phones. 

Does this contradict the phone company’s claim that the 5 colors are equally 

distributed 


8. Country A and Country B each have been competing in the 200-meter dash in the 

Olympics for many years. A random sample of 13 running times for Country A 

shows a mean of 24.52 seconds and a standard deviation of 0.76 seconds. A random 

sample of 13 running times for Country B shows a mean of 24.6 seconds and a 

standard deviation of 0.82 seconds. Assume times are normally distributed. 

a. Is there significant evidence to conclude that there is a difference between 

the average speed of the two groups Give appropriate statistical 

justification. 

b. Construct a 95% confidence interval for the difference between the average 

speeds of the two groups. Explain how this interval confirms or contradicts 

your conclusion in part a. 


9. A car dealer claimed that the average new car bought by people who live in 

Connecticut costs more than $25,000. A local newspaper thought that the claim was 

false, and the dealer was saying this so that they could justify charging higher prices. 

The newspaper took a random sample of 30 new car registrations in Connecticut and 

recorded the sales prices of those cars, which are given here. 

19,445 28,403 27,777 38,402 31,337 25,404 27,515 22,490 45,602 16,447 

Conduct the appropriate hypothesis test. Is the dealer’s statement supported by the data at 

the 0.10 significance level 

10. A researcher is studying whether there is a linear relationship between the number of 

“grow lights” used to illuminate an African Violet plant and the plant height in 

centimeters. The results of the regression are as shown in the following table. 

Predictor Coef SE Coef 

Constant 30.881 8.062 

Lights 10.953 3.948 

S = 8.49090 R-Sq = 46.1% R-Sq(adj) = 40.1% 

Number of observations = 11 

a. What is the regression equation that predicts plant height using number of lights 

b. Is the slope significant Calculate the value of the test statistic, compare it to the 

critical value of the test statistic, and make a conclusion. 

c. Construct a 90% confidence interval for β, using the given data.

1Final Exam Review

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