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.
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.
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
Related questions
Question
![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.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fc10cce41-ef51-4545-a724-9736e236d3b7%2F59328b15-53ac-4d98-935a-2dac2a9f975f%2F1s7rxyf.jpeg&w=3840&q=75)
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
![](/static/compass_v2/shared-icons/check-mark.png)
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
Step by step
Solved in 3 steps with 2 images
![Blurred answer](/static/compass_v2/solution-images/blurred-answer.jpg)
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