Question

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 of a large company wonders if this national average holds for the company's middle-aged male employees. The director examines the medical records of a random sample of 72 male employees in this age group and records each of their systolic blood pressure readings.

1. State an appropriate pair of hypotheses for a significance test in this setting. Be sure to define the parameter of interest.
2. Check conditions for performing the test in Question 1.
3. A 95% confidence interval for the mean systolic blood pressure of all 35- to 44-year-old employees at this company is (126.43, 133.43). Based on this interval, what conclusion would you make for a test of the hypotheses in Question 1 at the α = 0.05 significance level?

Answer 1

Solution-1:

Null hypothesis

Ho:

Null hypothesis In words

The mean systolic blood pressure of company's middle-aged male employees is 128

Alternative hypothesis

Ha:

the parameter of interest. is true mean systolic blood pressure for males  35 to 44 years of age

Alternative hypothesis In words

The mean systolic blood pressure of company's middle-aged male employees is not 128

parameter=population mean=mu=128

Check conditions for performing the test in Question 1.

sample should be random

sample should be independent

sample follows normal distribution

Here sample is simple random sample

sample szie,n=72

n>30

so according to central limit theorem sample follows normal distribution.

conditions for performing the t-test for mean are satisfied

Solution-3:

Given

A 95% confidence interval for the mean systolic blood pressure of all 35- to 44-year-old employees at this company is (126.43, 133.43).

Since the 95% confidence interval contains hypothesized mean value of 128

Decision;

Fail to reject null hypothesis

Accept null hypothesis

Conclusion:

There is sufficient statistical evidence at 5% level of significance to conclude that the mean systolic blood pressure

of company's middle-aged male employees is 128