Question

Suppose we take two different random samples from the same population of test scores. The population mean and standard deviation are unknown. The first sample has 25 data values. The second sample has 64 data values. Then we construct a 95% confidence interval for each sample to estimate the population mean. Which confidence interval will have greater precision (smaller width) for estimating the population mean?

Answer 1

The 95% confidence interval obtained with a sample size of 64 will give greater precision.

Explanation:

We are given the following in the question:

A 95% confidence interval is calculated with the following sample sizes

`n_1 = 25\\n_2 = 64`

The population mean and standard deviation are unknown.

Effect of sample size on confidence interval:

• As the sample size increases the margin of error decreases.
• As the margin of error decreases the width of the confidence level decreases.
• Thus, with increased sample size the width of confidence level decreases.

If we want a confidence interval with greater precision that is smaller width, we have to choose the higher sample size.

Thus, the 95% confidence interval obtained with a sample size of 64 will give greater precision.