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The Practice of Statistics for AP Examination

Daren Starnes, Josh Tabor

$Math Studyset Vaia Explanations$ Math

6th Edition · 837 pages

ISBN: 9781319113339

Chapter 10: Q 13. (page 640)

Ban junk food! A CBS News poll asked 606 randomly selected women and 442
randomly selected men, “Do you think putting a special tax on junk food would encourage more people to lose weight?” 170 of the women and 102 of the men said “Yes.” A 99% confidence interval for the difference (Women – Men) in the true proportion of people in each population who would say “Yes” is − $0.020 to 0.120$ . Does the confidence interval provide convincing evidence that the two population proportions are equal? Explain your answer.

Short Answer

Expert verified

It provides convincing evidence that two population proportions are equal.

Step by step solution

01

Given Information

It is given that at $99 %$ confidence interval, we got $(- 0.020, 0.120)$ .

02

Explanation

The given confidence interval has zero in it. Hence, it is likely that difference in proportion is zero and two population proportions are equal.

So, it is possible that population proportions are equal. Therefore, there is no convincing evidence that two population proportions are not equal.

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Most popular questions from this chapter

Flight times The pilot suspects that the Dubai-to-Doha outbound flight typically takes longer. If so, the difference (Outbound−Return) in flight times will be positive on more days than it is negative. What if either flight is equally likely to take longer? Then we can model the outcome on a randomly selected day with a coin toss. Heads means the Dubai-to-Doha outbound flight lasts longer; tails means the Doha-to-Dubai return flight lasts longer. To imitate a random sample of $12$ days, imagine tossing a fair coin $12$ times.

a. Find the probability of getting $11$ or more heads in $12$ tosses of a fair coin.

b. The outbound flight took longer on $11$ of the $12$ days. Based on your result in part (a), what conclusion would you make about the Emirates pilot’s suspicion?

Suppose the null and alternative hypothesis for a significance test are defined as

H0: μ= $40$ $\frac{305}{1526}$ $= 0.200 = 20.0 %$ H0 : μ= $40$

Ha: μ< $40$ $\frac{305}{1526} = 0.200 = 20.0 %$ Ha : μ< $40$

Which of the following specific values for Ha will give the highest power? a. μ= $38$ $\frac{305}{1526} = 0.200 = 20.0 %$ $μ = 38$

b. μ= $39$ $\frac{305}{1526} = 0.200 = 20.0 % μ = 39$

c. μ= $41$ $\frac{305}{1526} = 0.200 = 20.0 % μ = 41$

d. μ= $42$ $\frac{305}{1526} = 0.200 = 20.0 % μ = 42$

e. μ= $43$ $\frac{305}{1526} = 0.200 = 20.0 % μ = 43$

A study of the impact of caffeine consumption on reaction time was designed to correct for the impact of subjects’ prior sleep deprivation by dividing the $24$ subjects into $12$ pairs on the basis of the average hours of sleep they had had for the previous 5 nights. That is, the two with the highest average sleep were a pair, then the two with the next highest average sleep, and so on. One randomly assigned member of each pair drank $2$ cups of caffeinated coffee, and the other drank $2$ cups of decaf. Each subject’s performance on a Page Number: $690$ standard reaction-time test was recorded. Which of the following is the correct check of the “Normal/Large Sample” condition for this significance test?

I. Confirm graphically that the scores of the caffeine drinkers could have come from a Normal distribution.

II. Confirm graphically that the scores of the decaf drinkers could have come from a Normal distribution.

III. Confirm graphically that the differences in scores within each pair of subjects could have come from a Normal distribution.

a. I only

b. II only

c. III only

d. I and II only

e. I, I, and III

Each day I am getting better in math A "subliminal" message is below our threshold of awareness but may nonetheless influence us. Can subliminal messages help students learn math? A group of $18$ students who had failed the mathematics part of the City University of New York Skills Assessment Test agreed to participate in a study to find out. All received a daily subliminal message, flashed on a screen too rapidly to be consciously read. The treatment group of $10$ students (assigned at random) was exposed to "Each day I am getting better in math." The control group of $8$ students was exposed to a neutral message, "People are walking on the street." All $18$ students participated in a summer program designed to improve their math skills, and all took the assessment test again at the end of the program. The following table gives data on the subjects' scores before and after the program.

a. Explain why a two-sample t-test and not a paired t-test is the appropriate inference procedure in this setting.

b. The following boxplots display the differences in pretest and post-test scores for the students in the control (C) and treatment (T) groups. Write a few sentences comparing the performance of these two groups.

c. Do the data provide convincing evidence at the $α = 0.01, \frac{305}{1526} = 0.200 = 20 %$ significance level that subliminal messages help students like the ones in this study learn math, on average?

d. Can we generalize these results to the population of all students who failed the mathematics part of the City University of New York Skills Assessment Test? Why or why not?

The P-value for the stated hypotheses is $0.002$ Interpret this value in the context of this study.

a. Assuming that the true mean road rage score is the same for males and females, there is a $0.002$ probability of getting a difference in sample means equal to the one observed in this study.

b. Assuming that the true mean road rage score is the same for males and females, there is a $0.002$ probability of getting a difference in sample means at least as large in either direction as the one observed in this study.

c. Assuming that the true mean road rage score is different for males and females, there is a $0.002$ probability of getting a difference in sample means at least as large in either direction as the one observed in this study.

d. Assuming that the true mean road rage score is the same for males and females, there is a $0.002$ probability that the null hypothesis is true.

e. Assuming that the true mean road rage score is the same for males and females, there is a $0.002$ probability that the alternative hypothesis is true.

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