The manufacturer of hardness testing equipment uses steel-ball indenters to pene
ID: 3392344 • Letter: T
Question
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. The 95% confidence interval to judge whether the two indenters result in different measurements is 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.Explanation / Answer
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
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