Question

The data for a random sample of 8 paired observations are shown in the table to the right. Pair Population 1 53 37 24 Population 2 58 39 25 61 53 38 38 39 a. What are the appropriate null and alternative hypotheses to test whether the mean for population 2 is larger than that for population 1? b. Conduct the test identified in part a using α 0.01 c. Find a 99% confidence interval for μd. Interpret this result. d. What assumptions are necessary to ensure the validity of this analysis? 2 3 4 46 34 38 32 6 7 8

Answer 1

Null hypothesis: That is, the mean for population 2 is same as that for population 1 Alternative hypothesis That is, the mean for population 2 is larger than that for population1 Excel add-in (Mega Stat) procedure: Step 1: In EXCEL, Select Add-Ins> Mega Stat> Hypothesis Tests. Step 2: Choose Paired Observations. Step 3: Choose Data Input. Step 4: In Group 1, enter the column of Population 2. Step 5: In Group 2, enter the column of Population 1 Step 6: Enter 0 Under Hypothesized difference. Step 7: Check t-test, enter Confidence level as 99.0 Step 8: Choose greater than in alternative. Step 9: Click OK.

Excel add-in (Mega Stat) output: Hypothesis Test: Paired Observations 0.000 hypothesized value 43.875 mean Population 2 39.875 mean Population 1 4.000 mean difference (Population 2 Population 1) 2.726 std. dev 0.964 std. error 7 df 4.15 t 0021 p-value (one-tailed, upper) 0.628 confidence interval 99% lower 7.372 confidence interval 99% upper 3.372 margin of error The value oftest statistic is t=4.15 and the p-value is 0.0021 Conclusion

Use a significance level, α-001 Here, p-value is 0.0021, which is less than the value of α-0.01. That is, p-value(-0.0021)-α(-0.01) Therefore, by the rejection rule, reiect the null hvpothesis Ho Interpretation There is sufficient evidence at level of significance α 001 That is, the mean for population 2 is larger than that for population 1 The 99% confidence interval for is (0.628, 7.372). Interpretation It is 99% confident that the the confidence interval does not include the mean difference 0 then reject the null hypothesis That is, the mean for population 2 is larger than that for population1

Assumptions: The dependent variable must be continuous. The observations are independent of one another. The dependent variable should be approximately normally distributed. The dependent variable should not contain any outliers