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Construct a 95% confidence interval of the population standard deviation for the thickness of a plastic film (in mm) on a substrate material at 52°C

Construct a 95% confidence interval of the population standard deviation for the thickness of a plastic film (in mm) on a substrate material at 52°C

A First Course in Probability (10th Edition)
A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
Section: Chapter Questions
Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...
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Construct a 95% confidence interval of the population standard deviation for the 18. The thickness of a plastic film (in mm) on a substrate material is thought to be influenced by the temperature at which the coating is applied. In completely randomized experiment, 11 substrates are coated at 52°C, resulting in a sample mean coating thickness of 2.63 mm and a sample standard deviation of 0.26 mm. Another 13 substrates are coated at 66°C for which a sample mean of 2.53 mm and a sample standard deviation of 0.51 mm are observed. The Minitab output of the test for two variances is as given. Assume that the first and second samples given in the output are the substrates coated at 52°C and 66°C respectively. Assume also that the distribution of the thickness of plastic films is normal. Test and CI for Two Variances Method Null hypothesis Alternative hypothesis o (First)/o (Second) = 1 o (First)/o( Second) # 1 F method was used. This method is accurate for normal data only Statistics Sample St Dev Variances 95% CI for StDevs (0.182, 0.456) (0.366, 0.842) First 11 0.260 0.068 Second 13 0.510 0.260 Tests Test Statistic 0.26 Method DF1 DF2 P Value 10 12 0.041 thickness of a plastic film (in mm) on a substrate material at 52°C.
Transcribed Image Text:Construct a 95% confidence interval of the population standard deviation for the 18. The thickness of a plastic film (in mm) on a substrate material is thought to be influenced by the temperature at which the coating is applied. In completely randomized experiment, 11 substrates are coated at 52°C, resulting in a sample mean coating thickness of 2.63 mm and a sample standard deviation of 0.26 mm. Another 13 substrates are coated at 66°C for which a sample mean of 2.53 mm and a sample standard deviation of 0.51 mm are observed. The Minitab output of the test for two variances is as given. Assume that the first and second samples given in the output are the substrates coated at 52°C and 66°C respectively. Assume also that the distribution of the thickness of plastic films is normal. Test and CI for Two Variances Method Null hypothesis Alternative hypothesis o (First)/o (Second) = 1 o (First)/o( Second) # 1 F method was used. This method is accurate for normal data only Statistics Sample St Dev Variances 95% CI for StDevs (0.182, 0.456) (0.366, 0.842) First 11 0.260 0.068 Second 13 0.510 0.260 Tests Test Statistic 0.26 Method DF1 DF2 P Value 10 12 0.041 thickness of a plastic film (in mm) on a substrate material at 52°C.
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