Question

Alice prefers the rejection region method and Bob prefers the p-value method. If they are working on a 99\% confidence lower-tailed hypothesis test for a population proportion which of the following COULD happen? Assume Alice and Bob have correctly found the values for the test statistic, t, the cut off for the rejection region, -t* and the p-value, p.

Question 10 options:

Choose all that apply.

Alice finds that t<-t* and Bob finds that p<.01.

Alice finds that t<-t* and Bob finds that p>.01.

Alice finds that t>-t* and Bob finds that p>.01.

Alice finds that t>-t* and Bob finds that p<.01.

Answer 1

Solution:
Given in the question
The hypothesis test is left tailed hypothesis
Critical value or cutoff value is -t*, which means if test statistic value t is less than -t* than we will reject the null hypothesis else we will not reject the null hypothesis. (Alice finds that t<-t*)
Here alpha = 0.01, if the p-value is less than 0.01 than we will reject the null hypothesis else we will not reject the null hypothesis that means (bob finds that p<0.01)
So its correct answer is A i.e. Alice finds that t<-t* and bob finds that p<0.01