Chapter 8, Problem R8.9RE

a)

To determine

To explain: The condition required to construct the confidence interval using the t critical value rather than z .

Explanation of Solution

Z-distribution is used to compute the confidence interval for population mean when the value of the standard deviation is known. On the contrary, t -distribution is used to calculate the critical value when the sample standard deviation is known and the sample size is less than 30.

b)

To determine

To explain: The effect the increase of degree of freedom on t critical value for a particular confidence level.

Explanation of Solution

One of the properties of the t -distribution is that, the increase in degree of freedom makes the t -distribution to approach the normal distribution. Thus, it could be said that that the increase of degree of freedom makes the t critical value to approach the z critical value.