The manufacturer of hardness testing equipment uses steelbal

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. 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.)

Solution

Data

Hypothesized Difference

0

Level of Significance

0.05

Population 1 Sample

Sample Size

9

Sample Mean

60.3333

Sample Standard Deviation

8.1701

Population 2 Sample

Sample Size

9

Sample Mean

58.8889

Sample Standard Deviation

7.7046

Intermediate Calculations

Population 1 Sample Degrees of Freedom

8

Population 2 Sample Degrees of Freedom

8

Total Degrees of Freedom

16

Pooled Variance

63.0556

Standard Error

3.7433

Difference in Sample Means

1.4444

Confidence Interval Estimate

for the Difference Between Two Means

Data

Confidence Level

95%

Intermediate Calculations

Degrees of Freedom

16

t Value

2.1199

Interval Half Width

7.9355

Confidence Interval

Interval Lower Limit

-6.4910

Interval Upper Limit

9.3799

95 % Confidence intervals = (-6.5, 9.4)     ( round to nearest tenth)

There is insufficient evidence to conclude that the intenders produce different hardness readings.

( because 95% CI contains the value 0 )

Data
Hypothesized Difference	0
Level of Significance	0.05
Population 1 Sample
Sample Size	9
Sample Mean	60.3333
Sample Standard Deviation	8.1701
Population 2 Sample
Sample Size	9
Sample Mean	58.8889
Sample Standard Deviation	7.7046
Intermediate Calculations
Population 1 Sample Degrees of Freedom	8
Population 2 Sample Degrees of Freedom	8
Total Degrees of Freedom	16
Pooled Variance	63.0556
Standard Error	3.7433
Difference in Sample Means	1.4444