Q 3.2. - 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. 

Interpret the $95\%$ confidence interval in context. Explain how the confidence interval leads to the same conclusion as in Question $1$

Step-by-Step Solution

Answer

There is insufficient information to infer that the company's middle-aged male employees' mean blood pressure differs 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: Explanation

The $95$ percent confidence interval is calculated using the Minitab output $(126.43, 133.43)$ As a result, there is a $95\%$ likelihood that the mean systolic blood pressure of males aged $35-44$ falls between $126.43$ and $133.43$ Because $128$ is inside the estimated confidence interval. As a result, there is insufficient information to infer that the company's middle-aged male employees' mean blood pressure differs from the national average.