Question

The​ P-value for a hypothesis test is 0.081. For each of the following significance​ levels, decide whether the null hypothesis should be rejected.
a. alph-0.10 b. alpha=0.05

a. Determine whether the null hypothesis should be rejected for alphaequals0.10.
A. Reject the null hypothesis because the​ P-value is greater than the significance level.
B. Do not reject the null hypothesis because the​ P-value is greater than the significance level.
C. Do not reject the null hypothesis because the​ P-value is equal to or less than the significance level.
D. Reject the null hypothesis because the​ P-value is equal to or less than the significance level.

b. Determine whether the null hypothesis should be rejected for alphaequals0.05.
A. Reject the null hypothesis because the​ P-value is equal to or less than the significance level.
B. Reject the null hypothesis because the​ P-value is greater than the significance level.
C. Do not reject the null hypothesis because the​ P-value is greater than the significance level.
D. Do not reject the null hypothesis because the​ P-value is equal to or less than the significance level.

Answer 1

Let the level of significance be denoted by . The rule is that :-

• If P-value , the null hypothesis is rejected.
• If P-value , there is not enough evidence to reject the null hypothesis.

Given; P-value = 0.081

  =0.10 > P-value    D. Reject the null hypothesis because the​ P-value is equal to or less than the significance level.

  =0.05 < P-value    C. Do not eject the null hypothesis because the​ P-value is greater than the significance level.