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 100 children with chronic bronchitis are studied and their mean PEF is 292. Assume the population standard deviation is 75. 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. You MUST show your work to receive full credit. Partial credit is available. PLEASE TYPE ANSWER NOT A PHOTO!

Answer 1

H₀: $\mu$ = 306

H₁: $\mu$ < 306

The test statistic z = ($\bar x - \mu$)/()

a/Vn

                            = (292 - 306)/(75/)

100

                            = -1.87

At 0.05 significance level the critical value is z_0.05 = -1.645

Since the test statistic value is less than the critical value(-1.87 < -1.645), so we should reject the null hypothesis.

At 0.05 significance level, there is statistical evidence of a lower mean PEF in children with chronic bronchitis.