0.05. The population standard deviations are assumed to be known. After the sample data are collected, the test statisti

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0.05. The population standard deviations are assumed to be
known. After the sample data are collected, the test statistic is
computed to be z=2.54.
Complete parts a through c below.
a. Using the test statistic approach, what conclusion should be
reached about the null hypothesis?
Determine the critical​ value(s) for α=0.05. Select the
correct choice below and fill in the answer box to complete your
choice.
​(Round to two decimal places as​ needed.)
A.−zα= ____________
B.±zα/2=± ______________
C.zα= ______________
State the conclusion. Choose the correct answer below.
A. Do not reject the null hypothesis. There
is not sufficient evidence at α=0.05 to suggest that the
difference of the population means is different from 0.
B. Do not reject the null hypothesis. There is
sufficient evidence at α=0.05 to suggest that the difference of the
population means is different from 0.
C.Reject the null hypothesis. There is not sufficient
evidence at α=0.05 to suggest that the difference of the population
means is different from 0.
D.Reject the null hypothesis. There is sufficient evidence at
α=0.05 to suggest that the difference of the population means is
different from 0.
b. Using the p-value approach, what decision should be reached
about the null hypothesis?
Determine the​ p-value.
​p-value= ____________
​(Round to four decimal places as​ needed.)
State the conclusion. Choose the correct answer below.
A.Reject the null hypothesis. There is sufficient evidence at
α=0.05 to suggest that the difference of the population means is
different from 0.
B.Do not reject the null hypothesis. There is not
sufficient evidence at α=0.05 to suggest that the difference of the
population means is different from 0.
C.Reject the null hypothesis. There is not sufficient
evidence atα=0.05 to suggest that the difference of the population
means is different from 0.
D.Do not reject the null hypothesis. There is
sufficient evidence at α=0.05 to suggest that the difference of the
population means is different from 0.
c. Will the two approaches​ (test statistic and p-value)
ever provide different conclusions based on the same sample data?
Explain.
A.Yes, because it is possible for a test statistic in the
rejection region determined by the critical value(s) to have
a​ p-value greater than or equal to α.
B.No, because a test statistic in the rejection region
determined by the critical value(s) will always have
a​ p-value less than α.
C.No, because a test statistic in the rejection region
determined by the critical value(s) will always have
a​ p-value greater than or equal to α.
D.Yes, because it is possible for a test statistic not in the
rejection region determined by the critical value(s) to have
a​ p-value less than α.
H0​:
μ1−μ2=0
HA​:
μ1−μ2≠0