Question

A 95% confidence interval for a proportion is (0.103,0.297). Test the hypothesis that the population proportion is greater than 0.25. Be sure to include the 4 steps of an hypothesis test.

Answer 1

Now , The sample proportion is ,

p=(Upper confidence limit+Lower confidence limit)/2=(0.297+0.103)/2=0.20

The margin of error is ,

E=(Upper confidence limit-Lower confidence limit)/2=(0.297-0.103)/2=0.0970

Therefore , the sample size is ,

; From standard normal distribution table ,

1) Hypothesis : Vs  

2) The test statistic is ,

3) The critical value is ,

4) Decision : Here , the value of the test statistic does not lies in the rejection region.

Therefore , Fail to reject the Ho.

5) Conclusion : Hence , there is not sufficient evidence to suppot the claim that the population proportion is greater than 0.25