STATISTICS 115-The manufacturer of hardness testing equipment

1. The manufacturer of hardness testing equipment uses steel-ball indenters to penetrate metal that is being tested. However, the manufacturer thinks it would be better to use a diamond indenter so that all types of metal can be tested. Because of differences between the two types of indenters, it is suspected that the two methods will produce different hardness readings. The metal specimens to be tested are large enough so that two indentions can be made. Therefore, the manufacturer uses both indenters on each specimen and compares the hardness readings. Construct a 95% confidence interval to judge whether the two indenters result in different measurements.

Note: A normal probability plot and boxplot of the data indicate that the differences are approximately normally distributed with no outliers.

2 Click the icon to view the data table.

Construct a 95% confidence interval to judge whether the two indenters result in different measurements, where the differences are computed as 'diamond minus steel ball'.

The 95% confidence interval to judge whether the two indenters result in different measurements is ( , ). (Round to the nearest tenth as needed.)

State the appropriate conclusion. Choose the correct answer below.

There is sufficient evidence to conclude that the two indenters produce different hardness readings. There is insufficient evidence to conclude that the two indenters produce different hardness readings.

Specimen

1

2

3

4

5

6

7

8

9

Steel ball

51

57

61

71

68

54

65

51

53

Diamond

53

56

61

74

69

55

68

51

56

2. Assuming that both populations are normally distributed, test whether

?1 ? ?2 at the ? = 0.10 level of significance for the given sample data.

Population 1 Population 2

n 15 15

x 15.2 11.6

s 4.5 2.9

Should the null hypothesis be rejected?

A.

Yes, because the test statistic is not in the critical region.

B. No, because the test statistic is not in the critical region.

C. Yes, because the test statistic is in the critical region.

D. No, because the test statistic is in the critical region.

9. Assuming that both populations are normally distributed, construct a

Experimental

Control

90% confidence interval about ?1 ? ?2 . (?1 represents the mean of the

n

22

21

experimental group and ?2 represents the mean of the control group.)

x

45.5

40.7

s

4.3

13.4

The confidence interval has a lower bound of and an upper bound of . (Use ascending order. Round to two decimal places as needed.)