Question

You wish to test the following claim (Ha) at a significance level of α=0.10.

      Ho:p=0.71
      Ha:p>0.71

You obtain a sample of size n=277 in which there are 204 successful observations. For this test, you should use the (cumulative) binomial distribution to obtain an exact p-value. (Do not use the normal distribution as an approximation for the binomial distribution.)

What is the p-value for this sample? (Report answer accurate to four decimal places.)

p-value =

Answer 1

To Test :-

Ho:p=0.71
Ha:p>0.71

n = 277
P = X / n = 0.7365

Test Statistic :-


Z = 0.97

Test Criteria :-
Reject null hypothesis if

= 0.97 < 1.282, hence we fail to reject the null hypothesis
Conclusion :- We Fail to Reject H0

Decision based on P value
P value = P ( Z > 0.97 )
P value = 0.1660
Reject null hypothesis if P value <
Since P value = 0.166 > 0.1, hence we fail to reject the null hypothesis
Conclusion :- We Fail to Reject H0

There is insufficient evidence to support the claim that  p>0.71 at 10% level of significance.