Question

Two different groups in a statistics class are conducting a survey to estimate the mean number of units students at their college are enrolled in. The population mean and standard deviation are unknown. The sample from the first group survey has 49 data values. The sample from the second group survey has 81 data values. For each sample, the groups construct a 90% confidence interval to estimate the population mean. Which confidence interval will have greater precision (smaller width) for estimating the population mean

Answer 1

Answer:

Due to the larger sample size, the confidence interval of the second group will have greater precision for estimating the population mean.

Step-by-step explanation:

Margin of error of a confidence interval:

The equation for the margin of error of a confidence interval has the following format:

$M = z\frac{\sigma}{\sqrt{n}}$

In which z is related to the confidence level, $\sigma$ is the standard deviation of the population and n is the size of the sample.

From this, we can infer that a larger size leads to a greater precision of the interval, that is, a lesser margin of error.

In this question:

The sample from the first group survey has 49 data values, and from the second group has 81.

Due to the larger sample size, the confidence interval of the second group will have greater precision for estimating the population mean.