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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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