Question

Consider the following sample data drawn independently from normally distributed populations with equal population variances. Use Table 2. Sample 1 Sample 2 11.0 9.3 10.8 11.9 7.3 12.5 12.5 11.4 10.6 9.7 9.8 10.0 7.2 12.6 10.5 12.7 Click here for the Excel Data File a. Construct the relevant hypotheses to test if the mean of the second population is greater than the mean of the first population. H0: μ1 − μ2 = 0; HA: μ1 − μ2 ≠ 0 H0: μ1 − μ2 ≥ 0; HA: μ1 − μ2 < 0 H0: μ1 − μ2 ≤ 0; HA: μ1 − μ2 > 0 b-1. Calculate the value of the test statistic. (Negative values should be indicated by a minus sign. Round all intermediate calculations to at least 2 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. Using the critical value approach, can we reject the null hypothesis at the 1% significance level? Yes, since the value of the test statistic is less than the critical value of -2.624. Yes, since the value of the test statistic is less than the critical value of -2.977. No, since the value of the test statistic is not less than the critical value of -2.977. No, since the value of the test statistic is not less than the critical value of -2.624. c. Using the critical value approach, can we reject the null hypothesis at the 5% level? No, since the value of the test statistic is not less than the critical value of -1.761. Yes, since the value of the test statistic is less than the critical value of -1.345. Yes, since the value of the test statistic is less than the critical value of -1.761. No, since the value of the test statistic is not less than the critical value of -1.345.  

Answer 1

The statistical software output for this problem is:

Hence,

a) Hypotheses: H0: μ1 − μ2 ≥ 0; HA: μ1 − μ2 < 0

b - 1) Test statistic = -1.14

b - 2) Critical value = -2.624

b - 3) No, since the value of the test statistic is not less than the critical value of -2.624.

c) No, since the value of the test statistic is not less than the critical value of -1.761.