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Chapter 10: Q. 8 (page 667)

A beef rancher randomly sampled 42cattle from her large herd to obtain a 95%confidence interval to estimate the mean weight of the cows 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 and would have less precision than the original estimate.

(b) wider and would have more precision than the original estimate.

(c) wider and would have the same precision as the original estimate.

(d) narrower and would have less precision than the original estimate.

(e) narrower and would have more precision than the original estimate.

Short Answer

Expert verified

Wider and would have been less precision than original.

Step by step solution

01

Given information

We have been given98%confidence interval instead of a 95%confidence interval.

02

Explanation

As the confidence level increases, we will be more sure about the true mean thus it needs to contain more possible values which implies that confidence level is much wider.

As the confidence interval is wider , our estimate is less accurate.

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Most popular questions from this chapter

Your teacher brings two bags of colored goldfish crackers to class. She tells you that Bag 1has 25%red crackers and Bag 2has 35%red crackers. Each bag contains more than 500crackers. Using a paper cup, your teacher takes an SRS of 50crackers from Bag 1 and a separate SRS of 40crackers from Bag 2. Let p1^-p2^be the difference in the sample proportions of red crackers.

What is the shape of the sampling distribution ofp1^-p2^ ? Why?

Preventing drowning Drowning in bathtubs is a major cause of death in children less than 5 years old. A random sample of parents was asked many questions related to bathtub safety. Overall, 85% of the sample said they used baby bathtubs for infants. Estimate the percent of all parents of young children who use baby bathtubs.

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Refer to Exercise 15.

(a) Carry out a significance test at the 伪=0.05level.

(b) Construct and interpret a 95%confidence interval for the difference between the population proportions. Explain how the confidence interval is consistent with the results of the test in part (a).
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