Question

You wish to test the following claim (H1H1) at a significance level of α=0.02α=0.02.

      Ho:p=0.26Ho:p=0.26
      H1:p>0.26H1:p>0.26

You obtain a sample of size n=267n=267 in which there are 82 successful observations.

Answer 1

We have given
P0=0.26
n=267
x=82
P=82/267=0.3071
significance level of 0.02.

(a) What are the null and alternative hypotheses?
H0: P=P0
Ha: P > P0 Ha: P <P0

(b) What is the test statistic?
z=(P-P0)/sqrt(P0*(1-P0)/n)
=(0.3071-0.26)/sqrt(0.26*(1-0.26)/267)
=1.75

(c) What is the critical value?
2.3263

(d) Do you reject or fail to reject the null hypothesis? Explain your reasoning.

We do not reject the null hypothesis because
test statistic < critical value

Conclusion
There is no enough evidence against Ho hence we do not reject.