Question

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 H0:μ=175 millimeters versus H1:μ>175 millimeters, using the results of n samples. Find the boundary of the critical region if the type I error probability is α=0.05 and n=16.

Round your intermediate values to two decimal places. Round your answer to one decimal places (e.g. 98.76).

Answer 1

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 H0:μ=175 millimeters versus H1:μ>175 millimeters, using the results of n samples. Find the boundary of the critical region if the type I error probability is α=0.05 and n=16.

Round your intermediate values to two decimal places. Round your answer to one decimal places (e.g. 98.76).

Solution:

Given

n=16   

μ=175

= 20

α=0.05

H0:μ=175 millimeters

H1:μ >175 millimeters (one tail test or right tail test)

we have

df = n-1 =15

In this Question (sample mean) is not given. so we can not perform the hypothesis test

Here only asking the boundary of the critical region

The boundary of the critical region = t_{0.05 for 15 df and for one tail} =   1.753 Answer ( from t table)