Question

Peak expiratory flow (PEF) is a measure of a patient’s ability to expel air from the lungs. Patients with asthma or other respiratory conditions often have restricted PEF. The mean PEF for children free of asthma is 306. An investigator wants to test whether children with chronic bronchitis have restricted PEF. A sample of 50 children with chronic bronchitis are studied and their mean PEF is 281. Assume the population standard deviation is 69. Is there statistical evidence of a lower mean PEF in children with chronic bronchitis? Run the appropriate test at α=0.05. Give each of the following to receive full credit: 1) the appropriate null and alternative hypotheses; 2) the appropriate test; 3) the decision rule; 4) the calculation of the test statistic; and 5) your conclusion including a comparison to alpha or the critical value.

Answer 1

1

Hypothesis -

H0: >= 306

H1: < 0.306 (left tailed)

2)

Since population standard deviation is known, we use z test.

3)

Decision rule -

Critical value at 0.05 significance level = -1.645,

Reject H0 if test statistics < -1.645.

4)

Test statistics

z = - / / sqrt(n)

= 281 - 306 / 69 / sqrt(50)

= -2.56

This is test statistics value.

5)

Since test statistics value < -1.645, we have sufficient evidence to reject H0.

We conclude at 0.05 level that we have enough evidence to support the claim.