In testing the hypotheses H0: p = 0.5 vs Ha: p <= 0.5, suppose you get a p-value

Question

In testing the hypotheses H0: p = 0.5 vs Ha: p <= 0.5, suppose you get a p-value 0.022. Then
you realize that the one sided alternative is too restrictive and re-do the test with a two sided
alternative Ha : p =/= 0.5.

Based on the new p-value, what will be your conclusion ?

A. Fail to reject H0 at all the above alpha values.
B. Reject H0 at alpha = 0.05 and alpha = 0.1 but not at alpha = 0.01.
C. Reject H0 at alpha = 0.05 and alpha = 0.01 but not at alpha = 0.1.
D. Reject H0 at alpha = 0.01 but not at alpha = 0.05; 0.1.
E. Reject H0 at all the above alpha values.

Which of the following confidence intervals of p would contain
0.5 ?

A. Only 90%
B. Only 95%
C. 95% and 99% but not 90%
D. 90% and 99% but not 95%
E. 90%, 95% and 99% - all of them
F. None of 90%, 95% or 99%.
G. Only 99%
H. 90% and 95% but not 99%

Explanation / Answer

for two tailed test ; p value =2*0.022=0.044

as p value is less than 0.05 and 0.1 level but not 0.01 level

hence correct option is :

B. Reject H0 at alpha = 0.05 and alpha = 0.1 but not at alpha = 0.01.

2)Which of the following confidence intervals of p would contain
0.5 ?

G. Only 99%

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