Hypothesis testing for door thickness
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A door manufacturer wants to monitor the performance of a new painting process, which has been designed to apply paint with a mean thickness of 0.7mm, by detecting any departure from this target. One hundred doors will be randomly chosen from a day's production, and the thickness of paint on each of the 100 doors will be measured.
a) Explain how you would test whether the mean thickness of paint on the entire day's production meets the required standard of 0.7mm, using a .01 level of significance. Include all the following in your explanation:
i) whether the test will be one-tailed or two-tailed;
ii) how you would calculate a test statistic;
iii) how you would define the rejection region;
iv) any assumptions you would make;
v) how you would interpret the possible results of the test.
b) Suppose the mean thickness of paint on the 100 doors tested is 0.65mm and the standard deviation is .02mm. Use these data to conduct the test of hypothesis.
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Solution Summary
This solution details how to perform a hypothesis test to assert the thickness of doors produced from a manufacturer.
Education
- BSc , Wuhan Univ. China
- MA, Shandong Univ.
Recent Feedback
- "Your solution, looks excellent. I recognize things from previous chapters. I have seen the standard deviation formula you used to get 5.154. I do understand the Central Limit Theorem needs the sample size (n) to be greater than 30, we have 100. I do understand the sample mean(s) of the population will follow a normal distribution, and that CLT states the sample mean of population is the population (mean), we have 143.74. But when and WHY do we use the standard deviation formula where you got 5.154. WHEN & Why use standard deviation of the sample mean. I don't understand, why don't we simply use the "100" I understand that standard deviation is the square root of variance. I do understand that the variance is the square of the differences of each sample data value minus the mean. But somehow, why not use 100, why use standard deviation of sample mean? Please help explain."
- "excellent work"
- "Thank you so much for all of your help!!! I will be posting another assignment. Please let me know (once posted), if the credits I'm offering is enough or you ! Thanks again!"
- "Thank you"
- "Thank you very much for your valuable time and assistance!"
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