Question

www.helpyourmath.com is an OER website to help students to save money on textbooks and homeworksystems. A survey of 22 randomly selected students finds that they save a mean of $195 per semester byusing www.helpyourmath.com. Assume the date comes from a normal distribution and the samplestandard deviation is $10 per month.Confidence Interval: What is the 90% confidence interval to estimate the population mean? Round youranswers to two decimal places.191.50xXpe < 198.51х

Answer 1

Gven

A survey of 22 randomly selected students finds that they save a mean of $195 per semester.

Assume the data comes from a normal distribution and the sample standard deviation is $10 per month.

To find the 90% confidence interval to estimate the population mean, Round your answers to two decimal places.

Explanation:

It is given that,

$\begin{gathered} n=22 \\ \bar{x}=195 \\ s=10 \end{gathered}$

Then, the confidence interval is determined by,

$\begin{gathered} CI=\bar{x}\pm z\times\frac{s}{\sqrt{n}} \\ =195\pm1.6449\times\frac{10}{\sqrt{22}} \\ =195\pm3.507 \end{gathered}$

That implies,

$\begin{gathered} 195-3.507<\mu<195+3.507 \\ 191.493<\mu<198.507 \\ 191.50<\mu<198.51 \end{gathered}$

Hence, the confidence interval is,

$191.50\lt\mu\lt198.51$