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Chapter 8: Q 81. (page 543)

One reason for using a t distribution instead of the standard Normal distribution to find critical values when calculating a level C confidence interval for a population mean is that

a. zcan be used only for large samples.

b. zrequires that you know the population standard deviation 蟽.

c. z requires that you can regard your data as an SRS from the population.

d. z requires that the sample size is less than 10% of the population size.

e. a z critical value will lead to a wider interval than a t critical value.

Short Answer

Expert verified

Option (b) is correct.

Step by step solution

01

Given Information

We are given that

a. z can be used only for large samples.

b. z requires that you know the population standard deviation 蟽.

c. z requires that you can regard your data as an SRS from the population.

d. z requires that the sample size is less than 10% of the population size.

e. a z critical value will lead to a wider interval than a t critical value.

02

Explanation

To calculate confidence interval of population mean, zdistribution is used. This is used if standard deviation is known.

If standard deviation is known, tdistribution is used to find critical value.

Option (b) is correct.

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Most popular questions from this chapter

Critical values What critical value t*from Table B should be used for a confidence interval for the population mean in each of the following situations?

a. A 90% confidence interval based on n=12 randomly selected observations

b. A 95% confidence interval from an SRS of 30 observations

c. A 99% confidence interval based on a random sample of size 58

In a poll conducted by phone,

I. Some people refused to answer questions.

II. People without telephones could not be in the sample.

III. Some people never answered the phone in several calls.

Which of these possible sources of bias is included in the 卤2%margin of error announced for the poll?

a. I only

b. II only

c. III only

d. I, II, and III

e. None of these

How many pairs of shoes, on average, do female teens have? To find out, an AP Statistics class selected an SRS of 20female students from their school. Then they recorded the number of pairs of shoes that each student reported having. Here are the data:

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b. Do you think a 95%confidence interval for baby boomers would have a larger or smaller margin of error than the estimate from Exercise 42? Explain your answer.
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