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A consumer products company is formulating a new shampoo and is interested in foam height (in millimeters). Foam height is approximately normally distributed and has a standard deviation of 20 millimeters. The company wishes to test Ho: µ = 175 millimeters versus Hj: µ ± 175 millimeters, using the results of n= 10 samples.

A consumer products company is formulating a new shampoo and is interested in foam height (in millimeters). Foam height is approximately normally distributed and has a standard deviation of 20 millimeters. The company wishes to test Ho: µ = 175 millimeters versus Hj: µ ± 175 millimeters, using the results of n= 10 samples.

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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A consumer products company is formulating a new shampoo and is interested in foam height (in millimeters). Foam height is approximately normally distributed and has a standard deviation of 20 millimeters. The company wishes to test Ho: µ= 175 millimeters versus H1: µ + 175 millimeters, using the results of n = 10 samples. - v What is the type I error probability if the acceptance region is 155 < i< 195 ? a. Fail to reject Ho. The 10 samples may not be an appropriate sample size b.n should be lower than 10 samples - v If a = 0.05, would we need to reject the Ho? C. P(155 <x< 195, when u=156) = 0.5628 - v Find B for the case in which the true foam height is 156 millimeters d. Probability of committing Type I Error cannot be determined because a was not given e. Reject Ho v Find n if the probability of failing to reject a false null hypothesis is set at 0.05. And that the true foam height was found to be really 156 millimeters f. P(Type II Error) = 0.5 g. P(Type I Error) = 0.00157 h.nz 14
Transcribed Image Text:A consumer products company is formulating a new shampoo and is interested in foam height (in millimeters). Foam height is approximately normally distributed and has a standard deviation of 20 millimeters. The company wishes to test Ho: µ= 175 millimeters versus H1: µ + 175 millimeters, using the results of n = 10 samples. - v What is the type I error probability if the acceptance region is 155 < i< 195 ? a. Fail to reject Ho. The 10 samples may not be an appropriate sample size b.n should be lower than 10 samples - v If a = 0.05, would we need to reject the Ho? C. P(155 <x< 195, when u=156) = 0.5628 - v Find B for the case in which the true foam height is 156 millimeters d. Probability of committing Type I Error cannot be determined because a was not given e. Reject Ho v Find n if the probability of failing to reject a false null hypothesis is set at 0.05. And that the true foam height was found to be really 156 millimeters f. P(Type II Error) = 0.5 g. P(Type I Error) = 0.00157 h.nz 14
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