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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: u = 175 millimeters versus H.: u + 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: u = 175 millimeters versus H.: u + 175 millimeters, using the results of n= 10 samples.

Calculus For The Life Sciences
Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter13: Probability And Calculus
Section13.3: Special Probability Density Functions
Problem 28E
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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 H;: u + 175 millimeters, using the results of n = 10 samples. What is the type I error probability if the acceptance region is 155 s zS 195? a. P(155 sīS 195, when u= 156) = 0.5628 b. Reject Ho v If a = 0.05, would we need to reject the Ho? C. Probability of committing Type I Error cannot be determined because a was not given Find B for the case in which the true foam height is 156 millimeters d. Fail to reject Ho. The 10 samples may not be an appropriate sample size should be lower than 10 samples en Find n if the probability of failing to reject a false null hyporthesis is set at 0.05. And that the true foam height was found to be really 156 millimeters f. P(Type I| Error) = 0.5 g. P(Type I Error) = 0.00157 h.ns 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 H;: u + 175 millimeters, using the results of n = 10 samples. What is the type I error probability if the acceptance region is 155 s zS 195? a. P(155 sīS 195, when u= 156) = 0.5628 b. Reject Ho v If a = 0.05, would we need to reject the Ho? C. Probability of committing Type I Error cannot be determined because a was not given Find B for the case in which the true foam height is 156 millimeters d. Fail to reject Ho. The 10 samples may not be an appropriate sample size should be lower than 10 samples en Find n if the probability of failing to reject a false null hyporthesis is set at 0.05. And that the true foam height was found to be really 156 millimeters f. P(Type I| Error) = 0.5 g. P(Type I Error) = 0.00157 h.ns 14
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