2. A consumer product 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, o, of 10 millimeters. The company wishes to test the following hypotheses using the results of n=25 samples: Ho: μ = 160, H1: μ > 160 The critical region to reject the null hypothesis is X > 165 (a) Find the type I error probability a. (b) Find the probability of type II error if the true mean form height is 163 millimeters.

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2. A consumer product 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, o, of 10 millimeters. The company wishes to test the following
hypotheses using the results of n=25 samples:
Ho: μ = 160, Η: μ > 160
The critical region to reject the null hypothesis is X > 165
(a) Find the type I error probability a.
(b) Find the probability of type II error if the true mean form height is 163 millimeters.
Transcribed Image Text:2. A consumer product 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, o, of 10 millimeters. The company wishes to test the following hypotheses using the results of n=25 samples: Ho: μ = 160, Η: μ > 160 The critical region to reject the null hypothesis is X > 165 (a) Find the type I error probability a. (b) Find the probability of type II error if the true mean form height is 163 millimeters.
Expert Solution
Step 1

Given that

Sample size =25

Standard deviation =10

Null Hypothesis H0:μ=160

Alternative Hypothesis Ha:μ>160

Critical Region: reject null hypothesis if x̄>165

We have to find

a ..Type 1 error 

b .. probability of type 2 error if the true mean height is 163 millimetres

 

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