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) Find the type I error probability a if the critical region is x>185. (b) What is the probability of type II error if the true mean foam height is 185 millimeters? (c) Find B for the true mean of 195 millimeters.

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) Find the type I error probability a if the critical region is x>185. (b) What is the probability of type II error if the true mean foam height is 185 millimeters? (c) Find B for the true mean of 195 millimeters.

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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Question

Answer the exercise of the image.

(In the other image are the final answers, this to verify the final answer).

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) Find the type I error probability a if the critical region is
x>185.
(b) What is the probability of type II error if the true mean
foam height is 185 millimeters?
(c) Find B for the true mean of 195 millimeters.

a α-0.057053,
ь.В — 0.5,
c. B = 0.057053.

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