The standard deviation of a normal population is 10. You take a sample of 25 items from this...

Question:

The standard deviation of a normal population is 10. You take a sample of 25 items from this population and compute a 95% confidence interval.

In order to compute the confidence interval, you will use:

a. the t table because the degrees of freedom will be 24.

b. the t table because you have estimated the standard deviation from the sample.

c. the z table because the population standard deviation is known.

d. the z table because the sample size is small.

e. None of the above

Confidence Interval:

The confidence interval is an estimate of the population parameter, i.e., population mean. It gives the lower and upper values of the population parameter. The normal distribution is used when the sample size is large and the standard deviation of the population is known.

Given that,

Sample size, {eq}n = 25 {/eq}

Population standard deviation, {eq}\sigma = 10 {/eq}

The 95% confidence interval for the population mean is defined as:

{eq}\bar{x} \pm z_{0.05/2}\times \dfrac{s}{\sqrt{n}} {/eq}

The normal distribution is used to construct the confidence interval for the population mean when the standard deviation of the population is known. The z-table is used for the confidence coefficient.

Therefore, Option (c) is correct.