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Chapter 8: Q. R8.9 (page 548)

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 means?

b. For a particular level of confidence, explain what happens to the t critical values as Page Number: 548 the degrees of freedom increase.

Short Answer

Expert verified

Part a) When the sample standard deviation is known and the sample size is less than30, the t-distribution is used to calculate the critical value.

Part b) It could be said that as the degree of freedom increases, the tcritical value approaches the zcritical value.

Step by step solution

01

Part a) Step 1: The objective is to explain the condition required to construct the confidence interval using the t critical value rather than z

When the standard deviation is known, the Z-distribution is used to compute the confidence interval for the population mean.

When the sample standard deviation is known and the sample size is less than30, thet-distribution is used to calculate the critical value.

02

Part b) Step 2: The objective is to explain the effect the increase of the degree of freedom on tcritical value for a particular confidence level.

One of the t-properties distributions is that as the degree of freedom increases, the t-distribution approaches the normal distribution.

Therefore, It could be said that as the degree of freedom increases, the tcritical value approaches the zcritical value.

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