# Independent sample t test

Periodically Merrill Lynch customers are asked to evaluate Merrill Lynch¯Financial consultants and services (2000 Merrill Lynch Client Satisfactory Survey). Higher ratings on the client satisfaction survey indicate better service with 7 the maximum service

rating. Independent samples of service ratings for two ¯Financial consultants are summarized below. Consultant A has 10 years of experience while consultant B has 1 year of experience. Using a= .05, test to see whether the consultant with the more experience has the higher population mean service rating.

Consultant A Consultant B

x1 = 6.82 x2 = 6.25

s1 = .64 s2 = .75

n1 = 16 n2 = 10

a) State the null and the alternative hypotheses.

b) Compute the value of the test statistic.

c) What is the p-value?

d) What is your conclusion?

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#### Solution Summary

Step by step method for testing the hypothesis under 5 step approach is discussed here. Excel template for each problem is also included. This template can be used to obtain the answers of similar problems.

Independent sample t test

A manufacturer claims that the mean lifetime of its fluorescent bulbs is 1050 hours. A homeowner

selects 40 bulbs and finds the mean lifetime to be 1030 hours with a standard deviation of 80 hours.

Test the manufacturer's claim. Use α = 0.05

1. State H0

2. State Ha

3. What is the claim?

4. What is the critical value?

5. What is the standardized test statistic?

6. What is the decision?

A local politician, running for reelection claims the mean prison time for car thieves is less than the required four years. A sample of 80 convicted car thieves was randomly selected and the mean length of prison time was found to be 3.5 years with a standard deviation of 1.25 years. At α = 0.05 test the politician's claim.

7. State H0

8. State Ha

9. What is the claim?

10. What is the critical value?

11. What is the standardized test statistic?

12. What is the decision?

A local brewery distributes beer in bottles labeled 12 ounces. A government agency thinks the brewery is cheating its customers. The agency selects 20 of these bottles and measures their contents and obtains a mean of 11.7 ounces with a standard deviation of 0.7. At α = 0.01 test the claim.

13. State H0

14. State Ha

15. What is the claim?

16. What is the critical value?

17. What is the standardized test statistic?

18. What is the decision?

A medical researcher suspects that the pulse rate of smokers is higher than the pulse rate of non-smokers. Used the sample statistics below to test the researcher's suspicion. Use α = 0.05

Smokers Nonsmokers

n1 = 100 N2 = 100

x bar1 = 84 X bar2 =81

S1 = 4.8 S2= 5.3

19. State H0

20. State Ha

21. What is the claim?

22. What is the critical value?

23. What is the standardized test statistic?

24. What is the decision?

At α = 0.05, test a financial advisor's claim that the difference between the mean dividend rate for listings in the NYSE market and the mean dividend rate for listing in the NASDAQ market is more than 0.75. The sample statistics from randomly selected listings from each market are listed below.

NYSE NASDAQ

n1 = 30 n2 = 50

x bar1 = 2.75% x bar2 =1.66%

S1 = 1.44% S2= 0.63%

25. State H0

26. State Ha

27. What is the claim?

28. What is the critical value?

29. What is the standardized test statistic?

30. What is the decision?

31. Construct a 95% confidence interval for µ1 - µ2. Two samples are randomly selected from each

population . The sample statistics are given below.

n1 = 40 n2 = 35

x bar1 = 12 x bar2 =13

S1 = 2.5 S2= 2.8

A study was conducted to determine if the salaries of elementary school teachers from two neighboring districts are equal. A sample of 15 teachers from each school district was randomly selected. The mean from the first district was $28,000 with a standard deviation of $2,300. The mean from second school district was $30,300 with a standard deviation of $2,100. Test the claim that the salaries from both district are equal. Assume the variances are equal. Use α = 0.05.

32. State H0

33. State Ha

34. What is the claim?

35. What is the critical value?

36. What is the standardized test statistic?

37. What is the decision?

A local bank claims that the waiting time for its customers to be served is the lowest in the area. A competitor's bank checks the waiting time at both banks. The sample statistics are listed below. Test the local bank's claim assuming the variances are not equal. Use α = 0.05.

Local Bank Competitor Bank

n1 = 15 n2 = 16

x bar1 = 5.3 minutes x bar2 =5.6 minutes

S1 = 1.1 minutes S2= 1.0 minutes

38. State H0

39. State Ha

40. What is the claim?

41. What is the critical value?

42. What is the standardized test statistic?

43. What is the decision?

A manager wishes to determine the relationship between the number of miles (in hundreds of miles) the manager's sales representatives travel per month and the amount of sales (in thousands of dollars) per month.

Miles traveled, x 3 4 4 5 3 6 2 7 3

Sales, y 31 33 78 62 65 61 48 55 120

44. Find the linear regression.

45. Find the correlation coefficient.

46. Find the amount of sales if a sales rep traveled 10 miles.

47. If a sales rep made 80 in sales how many miles had they traveled?

The data below are the final exam scores of 10 randomly selected statistics students and the number of hours they studied for the exam.

Hours, x 3 5 2 8 2 4 4 5 6 3

Scores, y 65 80 60 88 66 78 85 90 90 71

48. Find the linear regression.

49. Find the correlation coefficient.

50. What grade did a student make if they studied 7 hours?

51. If a student made a 100 on the test how many hours had they studied?