Question

A professor wants to estimate how many hours per week her student‘s stUdy. A simple random sample of 56 students had a mean of 20 hours of studying per week. Construct a 95% confidence interval for the mean number of hours a student studies per week. Assume that the population standard deviation is known to be 2.3 hours per week. Round to two decimal places

Answer 1

Step-by-step explanation:

The formula for constructing a confidence interval is as follows:

`\begin{gathered} CI\bar{\text{ = x}}\pm\text{ MSE} \\ Where\text{ we are given that }\bar{x}\text{ = 20} \end{gathered}`
`\begin{gathered} MSE\text{ = z*}(\sigma)/(√(n)) \\ At\text{ 95\%, z = 1.960} \\ We\text{ are given that }\sigma\text{ = 2.3 and that n = 56} \\ MSE\text{ = 1.96 * }\frac{2.3\text{ }}{√(56)} \\ MSE\text{ = 0.6024....} \end{gathered}`

Answer: CI = (19.40 ; 20.60)