Consider the following competing hypotheses and accompanying sample data drawn i

Question

Consider the following competing hypotheses and accompanying sample data drawn independently from normally distributed populations. Use Table 2. H0: 1 2 0 HA: 1 2 < 0 formula43.mml = 251 formula44.mml = 252 s1 = 39 s2 = 19 n1 = 7 n2 = 7 a-1. Calculate the value of the test statistic under the assumption that the population variances are unknown but equal. (Negative values should be indicated by a minus sign. Round all intermediate calculations to at least 4 decimal places and final answer to 2 decimal places.) Test statistic a-2. Calculate the critical value at the 1% level of significance. (Negative value should be indicated by a minus sign. Round your answer to 3 decimal places.) Critical value a-3. Do you reject the null hypothesis at the 1% level? Yes, since the value of the test statistic is not less than the critical value. No, since the value of the test statistic is less than the critical value. No, since the value of the test statistic is not less than the critical value. Yes, since the value of the test statistic is less than the critical value. b-1. Calculate the value of the test statistic under the assumption that the population variances are unknown and are not equal. (Negative values should be indicated by a minus sign. Round intermediate calculations to at least 4 decimal places and final answer to 2 decimal places.) Test statistic b-2. Calculate the critical value at the 1% level of significance. (Negative value should be indicated by a minus sign. Round your answer to 3 decimal places.) Critical value b-3. Do you reject the null hypothesis at the 1% level? Yes, since the value of the test statistic is not less than the critical value. No, since the value of the test statistic is not less than the critical value. Yes, since the value of the test statistic is less than the critical value. No, since the value of the test statistic is less than the critical value.

Explanation / Answer

The statistical software output for this problem is:

Two sample T summary hypothesis test:
1 : Mean of Population 1
2 : Mean of Population 2
1 - 2 : Difference between two means
H0 : 1 - 2 = 0
HA : 1 - 2 < 0
(with pooled variances)

Hypothesis test results:

(without pooled variances)

Hypothesis test results:

Hence,

a - 1) Test statistic = -0.06

a - 2) Critical value = -2.681

a - 3) No, since the value of the test statistic is not less than the critical value.

b - 1) Test statistic = -0.06

b - 2) Critical value = -2.842

b - 3) No, since the value of the test statistic is not less than the critical value.

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