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 would you expect to have greater precision (smaller width) for estimating the population mean? (i) I expect the confidence interval based on the sample of 64 data values to be more precise. (ii) I expect both confidence intervals to have the same precision. (iii) I expect the confidence interval based on the sample of 25 data values to be more precise.

Answer 1

The correct option is (i) I expect the confidence interval based on the sample of 64 data values to be more precise.

Explanation:

Consider the provided information.

The sample size is inversely proportional to the standard error of the sample mean decreases.
`\sigma_M=(\sigma)/(N)`

As the size increase the standard error of the sample mean decreases.

Hence, for greater precision select the confidence interval based on the greater sample of data.

Therefore, we expect the confidence interval based on the sample of 64 data values to be more precise.

The correct option is (i) I expect the confidence interval based on the sample of 64 data values to be more precise.