Q 3.1. - The Practice of Statistics for AP

Question

The health director of a large company is concerned about the effects of stress on the company’s middle-aged male employees. According to the National Center for Health Statistics, the mean systolic blood pressure for males $35$ to $44$ years of age is $128$ The health director examines the medical records of a random sample of $72$ male employees in this age group. The Minitab output below displays the results of a significance test and a confidence interval. 

Do the results of the significance test allow us to conclude that the mean blood pressure for all the company’s middle-aged male employees differs from the national average? Justify your answer.

Step-by-Step Solution

Answer

No, It was not possible to determine whether the mean blood pressure of the company's middle-aged male employees differed from the national average.

Step 1: Given information

The output is: 

Step 2: Concept

$$\begin{gathered} H_0:\mu =0 \\ Ha:\mu \ne 0 \end{gathered}$$

Step 3: Calculation

The null and alternative hypotheses are: 

$$\begin{gathered} H_0 : \mu = 128 \\ {H}_a : \mu \ne 128 \end{gathered}$$

Here, $p -$value $(0.275) >\alpha (0.05)$ The null hypothesis is not rejected.

There is insufficient data to establish that the company's middle-aged male employees' mean blood pressure differs from the national average at a $5\%$ significance level.