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. |What is the type I error probability if the acceptance region is 1555 iS 195 ? a. P (155

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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.
|What is the type I eror probability if the acceptance region is 155 5 iS 195 ? a. P (155 <x< 195, when u=156) = 0.5628
b. Fail to reject Ho. The 10 samples may not be an appropriate sample size
v If a = 0.05, would we need to reject the Ho?
C.n should be lower than 10 samples
v Find B for the case in which the true foam height is 156 millimeters
d. P(Type I Error) = 0.00157
e. n2 14
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. Probability of committing Type I Error cannot be determined because
not given
was
g. P(Type II Error) = 0.5
h. Reject Ho
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. |What is the type I eror probability if the acceptance region is 155 5 iS 195 ? a. P (155 <x< 195, when u=156) = 0.5628 b. Fail to reject Ho. The 10 samples may not be an appropriate sample size v If a = 0.05, would we need to reject the Ho? C.n should be lower than 10 samples v Find B for the case in which the true foam height is 156 millimeters d. P(Type I Error) = 0.00157 e. n2 14 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. Probability of committing Type I Error cannot be determined because not given was g. P(Type II Error) = 0.5 h. Reject Ho
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