# Question: In order to compare the means of two populations independent

In order to compare the means of two populations, independent random samples of 400 observations are selected from each population, with the following results:

Sample 1 Sample 2

x̄1 = 5,275 .... x̄2 = 5,240

s1 = 150 ...... s2 = 200

a. Use a 95% confidence interval to estimate the difference between the population means (µ1 - µ2). Interpret the confidence interval.

b. Test the null hypothesis H0: (µ1 - µ2) = 0 versus the alternative hypothesis Ha: (µ1 - µ2) ≠ 0. Give the p-value of the test, and interpret the result.

c. Suppose the test in part b were conducted with the alternative hypothesis Ha: (µ1 - µ2) > 0. How would your answer to part b change?

d. Test the null hypothesis H0: (µ1 - µ2) = 25 versus the alternative Ha: (µ1 - µ2) = 25. Give the p-value, and interpret the result. Compare your answer with that obtained from the test conducted in part b.

e. What assumptions are necessary to ensure the validity of the inferential procedures applied in parts a–d?

Sample 1 Sample 2

x̄1 = 5,275 .... x̄2 = 5,240

s1 = 150 ...... s2 = 200

a. Use a 95% confidence interval to estimate the difference between the population means (µ1 - µ2). Interpret the confidence interval.

b. Test the null hypothesis H0: (µ1 - µ2) = 0 versus the alternative hypothesis Ha: (µ1 - µ2) ≠ 0. Give the p-value of the test, and interpret the result.

c. Suppose the test in part b were conducted with the alternative hypothesis Ha: (µ1 - µ2) > 0. How would your answer to part b change?

d. Test the null hypothesis H0: (µ1 - µ2) = 25 versus the alternative Ha: (µ1 - µ2) = 25. Give the p-value, and interpret the result. Compare your answer with that obtained from the test conducted in part b.

e. What assumptions are necessary to ensure the validity of the inferential procedures applied in parts a–d?

**View Solution:**## Answer to relevant Questions

Assume that σ12 = σ22 = σ2. Calculate the pooled estimator of σ2 for each of the following cases: a. s12 = 200, s22 = 180, n1 = n2 = 25 b. s12 = 25, s22 = 40, n1 = 20, n2 = 10 c. s12 = .20, s22 = .30, n1 = 8, n2 = 12 d. ...Refer to the Bulletin of Marine Science (April 2010) study of lobster trap placement, Exercise. Recall that the variable of interest was the average distance separating traps—called trap spacing —deployed by teams of ...A paired difference experiment produced the following data: a. Determine the values of t for which the null hypothesis µ1 - µ2 = 0 would be rejected in favor of the alternative hypothesis µ1 - µ2 < 0. Use α = .10. b. ...Determining alcoholic fermentation in wine is critical to the wine-making process. Must/wine density is a good indicator of the fermentation point, since the density value decreases as sugars are converted into alcohol. For ...A partially completed ANOVA table for a completely randomized design is shown here: a. Complete the ANOVA table. b. How many treatments are involved in the experiment? c. Do the data provide sufficient evidence to indicate a ...Post your question