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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. AP3.8 (page 702)

A beef rancher randomly sampled $42$ cattle from her large herd to obtain a $95 %$ confidence interval for the mean weight (in pounds) of the cattle in the herd. The interval obtained was ( $1010, 1321$ ). If the rancher had used a $98 %$ confidence interval instead, the interval would have been
a. wider with less precision than the original estimate.
b. wider with more precision than the original estimate.
c. wider with the same precision as the original estimate.
d. narrower with less precision than the original estimate.
e. narrower with more precision than the original estimate.

Short Answer

Expert verified

The correct option is (a) Wider with less precision than the original estimate

Step by step solution

01

Given Information

We have to determine the interval If the rancher had used a $98 %$ confidence interval instead .

02

Simplification

The confidence level rises when a

98

percent confidence interval is used instead of a

95

percent confidence interval.

As the confidence level rises, it is more likely that the confidence interval will contain the true mean, and as a result, the confidence interval will need to include all conceivable values for the mean, implying that the confidence interval will be bigger.

As the confidence interval widens, assessments such as confidence interval become more precise since the population mean has more plausible values.

Hence, the correct option is (a) Wider with less precision than the original estimate

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Most popular questions from this chapter

At a baseball game, $42$ of $65$ randomly selected people own an iPod. At a rock concert occurring at the same time across town, $34$ of $52$ randomly selected people own an iPod. A researcher wants to test the claim that the proportion of iPod owners at the two venues is different. A $90 %$ confidence interval for the difference (Game − Concert) in population proportions is $(- 0.154, 0.138)$ . Which of the following gives the correct outcome of the researcher’s test of the claim?

a. Because the confidence interval includes $0$ , the researcher can conclude that the proportion of iPod owners at the two venues is the same.

b. Because the center of the interval is $- 0.008$ , the researcher can conclude that a higher proportion of people at the rock concert own iPods than at the baseball game.

c. Because the confidence interval includes $0$ , the researcher cannot conclude that the proportion of iPod owners at the two venues is different.

d. Because the confidence interval includes more negative than positive values, the researcher can conclude that a higher proportion of people at the rock concert own iPods than at the baseball game.

e. The researcher cannot draw a conclusion about a claim without performing a significance test.

Shrubs and fire Fire is a serious threat to shrubs in dry climates. Some shrubs can

resprout from their roots after their tops are destroyed. Researchers wondered if fire would help with resprouting. One study of resprouting took place in a dry area of Mexico. The researchers randomly assigned shrubs to treatment and control groups. They clipped the tops of all the shrubs. They then applied a propane torch to the stumps of the treatment group to simulate a fire. All $12$ of the shrubs in the treatment group resprouted. Only $8$ of the $12$ shrubs in the control group resprouted.

a. State appropriate hypotheses for performing a significance test. Be sure to define the parameters of interest.

b. Check if the conditions for performing the test are met.

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

Where’s Egypt? In a Pew Research poll, $287$ out of $522$ randomly selected U.S. men were able to identify Egypt when it was highlighted on a map of the Middle East. When $520$ randomly selected U.S. women were asked, $233$ were able to do so.

a. Construct and interpret a $95 %$ confidence interval for the difference in the true

proportion of U.S. men and U.S. women who can identify Egypt on a map.

b. Based on your interval, is there convincing evidence of a difference in the true

proportions of U.S. men and women who can identify Egypt on a map? Justify your

answer.

Bag lunch? Phoebe has a hunch that older students at her very large high

school are more likely to bring a bag lunch than younger students because they have grown tired of cafeteria food. She takes a simple random sample of 80 sophomores and finds that $52$ of them bring a bag lunch. A simple random sample of $104$ seniors reveals that $78$ of them bring a bag lunch.

a. Do these data give convincing evidence to support Phoebe’s hunch at the $α = 0.05$ significance level?

b. Interpret the $P$ -value from part (a) in the context of this study.

See all solutions

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