Question

In a recent study of statistics students, a random sample of students were asked to provide the number of hours per week they spend studying for their statistics class. The results were used to compute confidence intervals for the population mean hours per week spent studying for statistics. The 95% confidence interval for the population mean hours per week that students spend studying for statistics was (6.83, 8.27). In this confidence interval, what is the sample mean (x bar) hours per week spent studying for statistics? Provide your answer as a number rounded to two decimal places.

Answer 1

The sample mean hours per week spent studying for statistics is 7.55 hours.

Explanation:

The (1 - α)% confidence interval for the population mean μ is:

`CI=\bar x\pm z_(\alpha/2)\ (\sigma)/(√(n))`

The 95% confidence interval for the population mean hours per week that students spend studying for statistics was (6.83, 8.27).

Compute the sample mean hours per week spent studying for statistics as follows:

`\frac{\text{UL + LL}}{2}=((\bar x+ z_(\alpha/2)\ (\sigma)/(√(n)))+(\bar x- z_(\alpha/2)\ (\sigma)/(√(n))))/(2)\\\\(8.27+6.83)/(2)=(2\cdot \bar x)/(2)\\\\7.55=\bar x`

Thus, the sample mean hours per week spent studying for statistics is 7.55 hours.