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# Hypothesis testing : T test

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6) In order to test the effects of replacing the bearings on different machines, ten different machines are chose. The number of parts produced in the hour before replacing the bearings and the number of parts produced in the hour after replacing the bearings is recorded. (Chart is on attachment).
A. Write the hypotheses that would be used to test the hypothesis that the production before replacing the bearings was greater than after replacing them.
B. Give the value of the test statistic and the p-value of the test:
t= p-value=
C. What is the decision?
D. Determine the 90% confidence interval for the difference in production per hour
E. What is the point estimate for the estimate for the difference in production from before and after the bearings are replaced?
F. What would you report to management as the effects of replacing the bearings?

7 a. How many randomly selected name brand computers would you need to estimate the mean price within +-\$140 with a 90% confidence, if prior knowledge tells you that (symbol on attachment) \$1,630? Show your work.
B. Name two ways you could reduce the required size of this sample.

8. In an effort to determine if level of education is a factor in the rate of layoff's the following data was gathered. Use a 0.05 level of significance to test independence.
(Chart on attachment)
A. State the hypotheses being tested.
B. The name of the test statistic is with degrees of freedom
C. Give the computed value of the test statistic.
D. What is the P-value of the test?
E. What is the critical value of the test statistic?
F. State and explain the decision.

##### Solution Summary

Step-by-step method for computing test statistic for t test is given in the answer.

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Hypotheses, p-values, confidence intervals
6) In order to test the effects of replacing the bearings on different machines, ten different machines are chose. The number of parts produced in the hour before replacing the bearings and the number of parts produced in the hour after replacing the bearings is recorded. (chart is on attachment)
A. Write the hypotheses that would be used to test the hypothesis that the production before replacing the bearings was greater than after replacing them.
H0: There is no significant difference in the mean number of parts produced before and after the replacement of bearings.
H1 : The mean number of parts produced after the replacement of bearings is higher than that of mean number of productions before the replacement.

B. Give the value of the test statistic and the p-value of the test:
The test statistic used is where is the mean of differences, S is the SD of differences
Rejection Criteria: Reject the null hypothesis, if value of test statistic is greater than the critical value of t.
Before After Before-After
198 194 4
187 192 -5
192 188 4
208 199 9
212 208 4
183 185 -2
203 199 4
196 195 1
172 178 -6
207 201 6

Paired-sample analysis for Before minus After

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