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t time When constructing confidence intervals for a population mean, we almost always

Chapter 8, Problem R8.10

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QUESTION:

t time When constructing confidence intervals for a population mean, we almost always use critical values from a t distribution rather than the standard Normal distribution. (a) When is it necessary to use a t critical value rather than a z critical value when constructing a confidence interval for a population mean? (b) Describe two ways that the t distributions are different from the standard Normal distribution. (c) Explain what happens to the t distributions as the degrees of freedom increase.

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QUESTION:

t time When constructing confidence intervals for a population mean, we almost always use critical values from a t distribution rather than the standard Normal distribution. (a) When is it necessary to use a t critical value rather than a z critical value when constructing a confidence interval for a population mean? (b) Describe two ways that the t distributions are different from the standard Normal distribution. (c) Explain what happens to the t distributions as the degrees of freedom increase.

ANSWER:

Step 1 of 3

(a)

We need to use the  critical value instead of a  critical value when we don't know the population standard deviation.

Then, we use the sample standard deviation,  to estimate the population standard deviation .

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