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Y have linear relation Y a X+ b, where a and b are real numbers? 3. A manufacturer produces piston rings for an automobile engine. It is known that ring diameter is approximately normally distributed with c-1.5mm. A random sample of 20 rings has a sample mean diameter of 75.012 mm and a sample standard deviation 1.25 mm. a. Can we conclude at.05 level of significance that the true mean piston diameter is at least 74.036 mm? Find the p-value of the test and make decision based on the p- value. b. Assume σ is not known. Find a 95% confidence interval for the population variance ơ2.

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Answer #1

a)

null hypothesis Alternate Hypothesis 74.036 74.036 for 0.05 level with right tailed test and n-1- 19 degree of freedom, critical value of t- Decision rule: 1.729 reject Ho if test statistic t>1.729 population mean sample mean sample size sample std deviation 74.036 75.01 20.00 1.250 μέ standard errror of meanS-s/Vn- 0.280 test staisic t 3.49 p value 0.0012

as p value is less then 0.05 level ; we reject null hypothesis and conclude that true mean piston diameter is at least 74.036.

b)

here n = 20 1.56 Critical value for 19 degree of freedom and 95 % Cl are as follows 8.907 0.025 32.852 UF Variance Cに (n-1)s/x Variance CI 0.904 心丬/w 3.333

from above 95% CI for variance =0.904 < sigma ^{2} <3.333

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