9. The Bethel Gear Company makes gears for car transmissions. Its parent company
ID: 2958627 • Letter: 9
Question
9. The Bethel Gear Company makes gears for car transmissions. Its parent company requires a gear diameter of 7.5 centimeters for the main transmission gear. In recent months the Bethel Gear Company has had a large number of gears rejected. The quality assurance manager believes the problem is caused by a lack of uniformity in the production line and asks the production team to implement a new production process. He then samples 25 gears and finds a mean of 7.51 and a standard deviation of 0.20. He wishes to test his claim that the new process is more uniform than the old process at a 10% level of significance. Historical records show that the mean for gear size over the last ten months has been exactly 7.49 with a standard deviation of 0.28. The quality assurance manager decides to use this data as the population mean and standard deviation as known population data.
a. State the claim the quality assurance manager is making mathematical symbols (µ, s, p, etc.). .
b. Based on this, what is the null hypothesis that the quality assurance manager would use to verify the claim?
c. State the alternative hypothesis for this claim using mathematical symbols.
d. What is the formula for the test statistic that the quality assurance manager would use to test the claim?
e. What table would the quality assurance manager use to test the claim? If degrees of freedom are involved, state the degrees of freedom that you would use in looking up the table value.
f. Draw a picture showing the distribution and the critical area of interest. Label the size in percent of the critical area, the critical value associated with the critical area, and the value of the test statistic.
g. State clearly if we should reject the null hypothesis or fail to reject it and also if the production team has indeed improved the uniformity of the product, using a 10% level of significance.
Explanation / Answer
Given =7.49, standard deviation== 0.28.
n=25. mean=xbar=7.51, standard deviation =s = 0.20
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