Question

A manufacturer of aircraft constant speed drives states that only 10% of their drives will fail before the scheduled overhaul interval. An airline performs a records check and finds that among 500 randomly selected constant speed drives, 90 failed before scheduled overhaul. Using a 2% significance level, test the manufacturer’s claim that the failure rate is 10%.

Answer 1

Below are the null and alternative Hypothesis,
Null Hypothesis: p = 0.1
Alternative Hypothesis: p ≠ 0.1

Rejection Region
This is two tailed test, for α = 0.02
Critical value of z are -2.33 and 2.33.
Hence reject H0 if z < -2.33 or z > 2.33

Test statistic,
z = (pcap - p)/sqrt(p*(1-p)/n)
z = (0.18 - 0.1)/sqrt(0.1*(1-0.1)/500)
z = 5.96

P-value Approach
P-value = 0
As P-value < 0.02, reject the null hypothesis.

Rejection Region Approach
As the value of test statistic, z is outside critical value range, reject the null hypothesis