Question

A survey of 400 statistics professors was undertaken. Each professor was asked how much time was devoted to teaching graphical techniques. We believe that the times are normally distributed with a standard deviation of 30 minutes. Estimate the population mean with 95% confidence.

Answer 1

We need to estimate the population mean with \(95 \%\) confidence, where a survey of 400 professors was asked how much time was devoted to teaching graphical techniques, considering these times are normally distributed with a standard deviation of 30 minutes.

That is,

The sample size is \(n=400\),

The population standard deviation is \(\sigma=30\) minutes.

Use MINITAB to construct the confidence interval for the given data of times taken for teaching graphical analysis using the following steps:

Step1: Import the data into one column named Time.

Step2: Click Start, Basic Statistics, and 1-Simple Z.

Step3: Type or Use the Select button to specify the name of the variable or the column it is stored in. In the samples in the columns box (Cost), type the value of the population standard deviation (30), and click Options...

Step4: Type the value of the confidence level \((0.95)\) and the Alternative box select not equal.

The resultant confidence interval is shown below:

Therefore, we can say that the mean time taken for teaching graphical techniques will lie between ( 249.44, 255.31) with 95% confidence.