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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 98percent confidence interval is used instead of a 95percent 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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