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AP Statistics Exam Review
Topic VII: Confidence Intervals and Significance Testing
1. A hypothetical golf ball manufacturer randomly selects a sample of 50 balls from a recently
manufactured batch and finds the mean diameter to be 1.25 inches with a standard deviation of 0.026
inches. What is the 95°/o confidence interval for the mean diameter?
2.
A. {1.2009, 1.2991)
B. {1.1855, 1.3145)
D. {1.2426, 1.2574)
E None of the above
c. (1.2405, 1.2595)
A hypothetical golf ball manufacturer randomly selects a sample of 50 balls from a recently
manufactured batch and finds the mean diameter to be 1.25 inches with a standard deviation of
0.026 inches. The 95% confidence level is calculated. Which of the following statements is a correct
interpretation of the confidence interval?
A.
There is a 95% chance that the confidence interval contains the population parameter.
B.
There is a 95% chance that the sample statistic ls contained in the confidence interval.
C.
for all possible samples of size 50, 95°/o of the confidence intervals constructed around the
sample statistic will contain the population parameter.
D. There is a 95% probability that a golf ball, chosen at randomr will have a diameter that falls into
this interval.
E. None of the above
3.
Which of the following statements correctly describes the P-value?
A.
The P-value represents the probability that the sample mean obtained is equal to the population
mean.
B. The P-value represents the probability, assuming the null hypothesis is correct, of obtaining results
at least as extreme as those actually obtained.
C. The P-value represents the probability that the results obtained are statistically significant.
D. All of the above are correct.
E. None of the above is correct.
4.
A hypothetical candy manufacturer claims that the weight of each bag of candy produced is 25 grams with
a standard deviation of 5 grams. You take a random sample of 50 bags and find that the mean weight of
the sample is 23.5 grams. What is the P- value for obtaining such a result from a population where the
weight of each candy bag is claimed to be 25 grams? Is there evidence at the 0.05 significance level that
the candy bags actually weigh less than 25 grams?
A.
0.2397; No, there is insufficient evidence to suggest that each of the bags weigh less than 25
grams each, since P-value = 0.2397 > a = 0.05.
B
0.0194; Yes, since P-value = 0.0194 < a = 0.05, there is evidence to suggest that each of the
bags weigh less than 25 grams.
C.
0.0345; Yes, since P-value = 0.0345 <a= 0.05, there is evidence to suggest that each of the
bags weigh less than 25 grams.
D.
0.1523; No, since P-value = 0.1523 <a= 0.05, there is insufficient evidence to suggest that
each of the bags weigh less than 25 grams.
E. None of the above are correct.
Use the following information for questions 5 - 7
A television station claims -that they broadcast fewer than 12 minutes of commercials every half hour.
You decide to test the claim by counting the number of minutes devoted to commercials for
randomly selected half-hour intervals during the day. You find that the commercial time per half
hour (ln minutes} is: 13, 14, 15, 10, 9,12, 14, 11, 10, 12, 16, 9,10, 13, 14.
5.
What are the null and alternative hypotheses?
A. Ho: µ >12 (The television station broadcasts more than 12 minutes of commercials every half-hour.)
Ha: µ < 12 (The television station broadcasts fewer than 12 minutes of commercials every half -hour.)
B. Ho: µ < 12 (The television station broadcasts at least 12 minutes of commercials every half-hour.)
Ha: µ < 12 (The television station broadcasts fewer than 12 minutes of commercials every half-hour.)
C. Ho: µ = 12 (The television station broadcasts 12 minutes of commercials every half-hour.)
Ha: µ< 12 (The television station broadcasts at most 12 minutes of commercials every half-hour.)
D. Ho: µ < 12 (The television station broadcasts fewer than 12 minutes of commercials every half -hour.)
Ha: µ > 12 (The television station broadcasts more than 12 minutes of commercials every half-hour.)
E. A hypothesis test is inappropriate in this situation.
6.
What is the test statistic? What is the P-value?
A.
t = 0.015; P-value = 0.5058
B.
z = 0.015; P-value = 0.5061
C.
t = 0.231; P-value = 0.5898
D.
z = 0.238; P-value = 0.5940
E.
t = -0.4178; P-value = 0.6588
7. What is the critical value? What can you conclude at the 0.1 significance level?
A.
t* = 1.341; Since the P-va!ue equals 0.51 and is greater than 0.01, there is insufficient
evidence to reject the null hypothesis. The claim appears to be accurate.
B.
t* = 1.761; Since the P-value equals 0.59 and is greater than 0.01, there is insufficient
evidence to reject the null hypothesis. The claim appears to be accurate.
C.
t* = 1.345; Since the P-value equals 0.51 and is greater than 0.01, there is insufficient
evidence to reject the null hypothesis. The claim appears to be. accurate.
D. t* = 0.692; Since the P-value equals 0.59 and is greater than 0.01, there is insufficient
evidence to reject the null hypothesis. The claim appears to be accurate.
E. z* = 0.238; Since the P-value is greater than 59, which is greater than 0.01, there is insufficient
evidence to reject the null hypothesis. The claim appears to be accurate.
Use the following information for questions 8 – 10:
You're conducting a survey to compare the price per gallon of gasoline in more- and less-affluent areas of a
large city. You choose 25 service stations in each area and calculate the mean price of gasoline for each
group. In less-affluent areas, you find that the mean price per gallon is $1.85, J11, with a standard deviation
of $0.25. In more-affluent areas, the mean price per gallon is $1.65, Jlz 1 with a standard deviation of
$0.35. An investigator for the local depa1tment of consumer affairs wishes to use the data you obtained from
this survey to determine whether the price of gas in less- affluent areas is significantly higher than in moreaffluent areas.
8. What are the null and alternative hypotheses for this investigation?
A. Ho: µ1- µ2 > 0, Ha µ1- µ2 < 0
B. Ho: µ1- µ2 = 0, Ha µ1- µ2 < 0
C. Ho: µ1- µ2 = 0 Ha: µ1- µ2 > 0
D. H0: µ1+ µ2 = 0, Ha: µ1- µ2 > 0
E. None of the above
9. W hat are the t statistic and P-value for the hypothesis test? What can you conclude?
A.
t = 2.32 and P-value = 0.99; Gas prices do not appear to be significantly higher in less-affluent
areas of this city.
B.
t = 2.32 and P-value = 0.012; There is evidence to conclude at the 0.05
significance level that gas prices may be significantly higher in less-affluent areas.
C.
t = 2.32 and P-value = 0.012; There is not sufficient evidence to conclude at the 0.05
significance level that gas prices may be significantly higher in less-affluent areas.
D. t = 2.32 and P-value = 0.025; There is evidence to conclude at the 0.05
significance level that gas prices may be significantly higher in less-affluent areas.
E.
None of the above
10. What is the 95°/o confidence interval for the difference ln gas prices, using the conservative degrees of
freedom?
A. (0.0401, 0.3599)
B. (-0.0317, 0.4320)
D. (0.0556, 0.5879)
E. (0.1562, 0.5491)
C. (-0.0078, 0.4089)
Use the following information for problems 11-12.
A survey by a high school newspaper indicates that 75% of the students (N = 1,500) saw the movie The Matrix.
You think the true percentage of students who saw it is lower. You survey 150 randomly selected students and find
that 100 of them saw the movie.
1 1 . Assuming a one-proportion z test is appropriate in this situation/ what are the null hypothesis, the test statistic,
and the P-value?
A. The null hypothesis is H0 : p = 0.75; z = -2.357, P-value = 0.009.
B. The null hypothesis is H0 : p = 0.75; z = -2.357, P-value = 0.018.
C. The null hypothesis is Ho: p < 0.75; z = -2.357, P-value = 0.991.
D. A one-proportion z test is not appropriate in this situation.
E. None of the above
12. Assuming that a one-proportion z test is appropriate for this situation, which of the following
conclusions can you draw at the 0.01 significance level?
A. Since P-va!ue = 0.009 < 0.01, reject the null hypothesis. There is evidence at the 0.01 significance level
that fewer than 75°/o of the students at this high school sawthe movie The Matrix.
B.
Since P-value = 0.018 > 0.01, do not reject the null hypothesis. There is insufficient evidence
that fewer than 75% of the students at this high school saw the movie The Matrix.
C.
Since P-value = 0.991> 0.01, do not reject the null hypothesis.There is insufficient evidence that
fewer than 75°/o of the students at this high school saw the movie The Matrix.
D. Since P-value = 0.009 < 0.01, do not reject the null hypothesis. There is no evidence at the 0.01
significance level that fewer than 75°/o of the students at this high school saw the movie The
Matrix.
E.
None of the above
13.
Which of the following are true statements about 𝑥 2 tests?
I.
𝑥 2 tests can be used to test whether the difference in two proportions is statistically significant.
II.
𝑥 2 tests can be used to establish the relationship between two categorical variables.
III.
𝑥 2 tests allow us to judge if observed data are consistent with expected patterns for that data.
A. I only
14 .
B. IIonly
c. III only
D. I and II only
E. II and III only
A teacher has designed a math test she thinks will predict an average student's performance in Algebra I. She
administers the test to a group of randomly selected students who have successfully completed a pre-algebra
course with average grades and then records the test scores. At the end of the year she records each student's final
math grade. Data for the hypothetical study is listed below:
Test score: 53, 48, 39, 72, 64, 69, 23 1 78, 36, 85
Final math grade: 56, 64, 76, 94r 81, 79, 88, 97, 55, 79
What is a least-squares regression line for the data? What is the correlation coefficient?
A.
B.
C.
D.
E.
y = 55.86 + 0.4386 x; r = 0.81
y = 34.95 + 10.57 x; r = 0.30
y = 13.26 + 0.565 x; r = 0.41
y = 60.019 + 0.2977 x; r = 0.41
y = 58.24 + 1.2977 x; r = 0.55
15.
Which of the following is not an assumption that must be checked when conducting a significance test for the
slope of a regression line?
A. There must be a linear relationship between the variables.
B. There must be equal variances in the distribution of the x variable.
C. There must be equal variances in the distribution of they variable.
D. There must be normality of response variables at each value of x.
E. All of the above are assumptions that must be checked when conducting this test.
16.
You construct a 95°/a confidence interval (that contains zero) around the slope of a regression line. Which of the
following is a valid conclusion?
A. The confidence interval is invalid.
B. There appears to be no linear relationship between the two variables.
C. There appears to be a linear relationship between the two variables.
D. There appears to be a nonlinear relationship between the two variables
E. None of the above
FREE RESPONSE
I.
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 manipulative
85
75
83
87
80
79
88
94
87
82
Without Manipulatives
78
84
81
78
76
83
79
75
85
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.
II.
A county legislator is interested in polling her constituents to estimate the difference between the positions of men and
women regarding a proposed bill to restrict cell phone use while driving. Her administrative assistants draw two samples,
one consisting of 500 men and the other consisting of 500 women. The survey indicates that 230 men and 194women
favor legislation that would restrict the use of cell phones while driving.
A.
Construct a 95% confidence interval to estimate the true difference between the proportions of men and women
who favor legislation that restricts cell phone use while driving
B.
Write one or two statements to a non-statistician explaining what is meant by the 95% confidence interval found
in part (A)
C.
How does a 99% confidence interval for the same data compare to the 95% confidence interval?