Question

1. Interstate Batteries are supposed to last at least 3 years. A consumer advocate collects a random sample of 200 of these batteries and finds that 186 last at least 3 years. Does this provide evidence at the 5% significance level to support the claim that less than 95% of all Interstate batteries last at least 3 years? Justify by running a hypothesis test.

Answer 1

Null and alternative hypotheses

Ho : p = 0.95

H1 : p < 0.95

Test statistic Z

Z = ( p^ - p)/ sqrt [ p *(1-p)/n]

Where p^ = 186/200 = 0.93

Z = (0.93 - 0.95)/sqrt [ 0.95*0.05/200]

Z = -1.30

Zcritical for a = 0.05 and left tailed test

Zcritical = Z​​​​​​a = Z​​​​​​0.05 = -1.645

Decision rule : If Z < -1.645 we reject the null hypothesis otherwise we fail to reject the null hypothesis

Our Z = -1.30 > -1.645

Decision : we fail to reject the null hypothesis Ho

Conclusion : There is no sufficient evidence to support the claim that less than 95% of all Interstate batteries last at least 3 years