1. Show all your work. Indicate clearly the methods you use, because you will be scored on thecorrectness of your methods as well as on the accuracy and completeness of your results andexplanations. A recent survey collected information on television viewing habits from a random sample of 1,000people in the United States. Of those sampled, 37 percent indicated that their favorite sport to watch ontelevision was American football. (a) Construct and interpret a 95 percent confidence interval for the proportion of all people in the UnitedStates who would indicate that their favorite sport to watch on television is American football. Please respond on separate paper, following directions from your teacher. (b) Based on your answer to part (a), is it reasonable to believe that 33 percent is the actual percent ofpeople in the United States whose favorite sport to watch on television is American football? Justifyyour answer. Please respond on separate paper, following directions from your teacher. 2. Show all your work. Indicate clearly the methods you use, because you will be scored on thecorrectness of your methods as well as on the accuracy and completeness of your results andexplanations. A fair die, with its faces numbered from to , is one in which each number is equally likely to landface up when the die is rolled. On a fair die, the probability that the number will land face up is . Agroup of students wanted to investigate a claim about manipulating a fair die so that it favors oneoutcome. The claim states that if a fair die is put into an oven and baked at for minutes, theinside of the die will begin to melt. When the die cools, the inside will be solid again, but with moreweight toward the bottom. This shift in weight will cause the face that was up when the die cooled toland up more often that the other faces.The students obtained a fair die and baked it according to the preceding directions. The die cooled withthe number face up. After the die cooled, they rolled the die times, and the number landed faceup times. Let represent the population proportion of times the number will land face up on thebaked die if the die could be rolled an infinite number of times. AP Statistics Test Booklet Unit 6 Progress Check: FRQ Copyright © 2021. The College Board. These materials are part of a College Board program. Use or distribution of these materials online or in print beyond yourschool’s participation in the program is prohibited. Page 2 of 3(a) Clarke, one of the students, constructed a percent confidence interval for as .Does the interval provide convincing statistical evidence that the number will land face up more oftenon the baked die than on a fair die? Explain your reasoning. Please respond on separate paper, following directions from your teacher. (b) Aurelia, another student, suggested they conduct a significance test to investigate the claim. Shetested the hypotheses versus at the significance level of . Sheobtained a test statistic of with a -value of . Do the results of the significance test agreewith the results of Clarke’s confidence interval in part (a)? Explain your reasoning. Please respond on separate paper, following directions from your teacher. (c) Two standard normal curves are shown below, one for the confidence interval calculated in part (a)and one for the significance test conducted in part (b).(i) For the confidence interval curve, label the critical values for the confidence level and shadethe area that represents values in the outer .(ii) For the significance test curve, label the critical value for the significance level and shade thearea representing the values of that would lead to a rejection of the null hypothesis in part (b). Please respond on separate paper, following directions from your teacher. (d) Joachim, a third student, noted that the confidence interval in part (a) gives plausible values of theparameter as an interval between two values. He suggested that they develop a one-sided confidenceinterval because they were only concerned with whether the number was landing face up more oftenthan expected, not less often. The one sided-interval will determine a value such that all plausiblevalues of are greater than . The formula for is .(i) Determine the values of needed to create the one-sided percent confidence interval. Thencalculate the value of . AP Statistics Test Booklet Unit 6 Progress Check: FRQ Copyright © 2021. The College Board. These materials are part of a College Board program. Use or distribution of these materials online or in print beyond your school’s participation in theprogram is prohibited. Page 3 of 3(ii) Do the results of Joachim’s one-sided confidence interval agree with results of Aurelia’ssignificance test in part (b)? Explain your reasoning.
1. Show all your work. Indicate clearly the methods you use, because you will be scored on the
correctness of your methods as well as on the accuracy and completeness of your results and
explanations.
A recent survey collected information on television viewing habits from a random sample of 1,000
people in the United States. Of those sampled, 37 percent indicated that their favorite sport to watch on
television was American football.
(a) Construct and interpret a 95 percent confidence interval for the proportion of all people in the United
States who would indicate that their favorite sport to watch on television is American football.
Please respond on separate paper, following directions from your teacher.
(b) Based on your answer to part (a), is it reasonable to believe that 33 percent is the actual percent of
people in the United States whose favorite sport to watch on television is American football? Justify
your answer.
Please respond on separate paper, following directions from your teacher.
2. Show all your work. Indicate clearly the methods you use, because you will be scored on the
correctness of your methods as well as on the accuracy and completeness of your results and
explanations.
A fair die, with its faces numbered from to , is one in which each number is equally likely to land
face up when the die is rolled. On a fair die, the probability that the number will land face up is . A
group of students wanted to investigate a claim about manipulating a fair die so that it favors one
outcome. The claim states that if a fair die is put into an oven and baked at for minutes, the
inside of the die will begin to melt. When the die cools, the inside will be solid again, but with more
weight toward the bottom. This shift in weight will cause the face that was up when the die cooled to
land up more often that the other faces.
The students obtained a fair die and baked it according to the preceding directions. The die cooled with
the number face up. After the die cooled, they rolled the die times, and the number landed face
up times. Let represent the population proportion of times the number will land face up on the
baked die if the die could be rolled an infinite number of times.
AP Statistics Test Booklet
Unit 6 Progress Check: FRQ
Copyright © 2021. The College Board. These materials are part of a College Board program. Use or distribution of these materials online or in print beyond your
school’s participation in the program is prohibited. Page 2 of 3
(a) Clarke, one of the students, constructed a percent confidence interval for as .
Does the interval provide convincing statistical evidence that the number will land face up more often
on the baked die than on a fair die? Explain your reasoning.
Please respond on separate paper, following directions from your teacher.
(b) Aurelia, another student, suggested they conduct a significance test to investigate the claim. She
tested the hypotheses versus at the significance level of . She
obtained a test statistic of with a -value of . Do the results of the significance test agree
with the results of Clarke’s confidence interval in part (a)? Explain your reasoning.
Please respond on separate paper, following directions from your teacher.
(c) Two standard normal curves are shown below, one for the confidence interval calculated in part (a)
and one for the significance test conducted in part (b).
(i) For the confidence interval curve, label the critical values for the confidence level and shade
the area that represents values in the outer .
(ii) For the significance test curve, label the critical value for the significance level and shade the
area representing the values of that would lead to a rejection of the null hypothesis in part (b).
Please respond on separate paper, following directions from your teacher.
(d) Joachim, a third student, noted that the confidence interval in part (a) gives plausible values of the
parameter as an interval between two values. He suggested that they develop a one-sided confidence
interval because they were only concerned with whether the number was landing face up more often
than expected, not less often. The one sided-interval will determine a value such that all plausible
values of are greater than . The formula for is .
(i) Determine the values of needed to create the one-sided percent confidence interval. Then
calculate the value of .
AP Statistics Test Booklet
Unit 6 Progress Check: FRQ
Copyright © 2021. The College Board. These materials are part of a College Board program. Use or distribution of these materials online or in print beyond your school’s participation in the
program is prohibited. Page 3 of 3
(ii) Do the results of Joachim’s one-sided confidence interval agree with results of Aurelia’s
significance test in part (b)? Explain your reasoning.
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