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 millimeters versus millimeters, using the results of n samples. Find the boundary of the critical region if the type I error probability is and

Answer 1

Complete 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: u=175 millimeters versus Ha:u>175 millimeters, using the results of n samples. Find the boundary of the critical region if the type I error probability is
`\alpha = 0.01` and n = 16

Answer:

186.63

Explanation:

Given:

`\alpha = 0.01`

Using the standard normal deviate table:

NORMSINV(0.01) = 2.326

Thus, the Z score = 2.326

To find the critical value if the mean, use the formula:

`(X' - u_0)/(\sigma/√(n)) = Z`

Since we are to find X', Make X' subject of the formula:

`X' = u_0 + (Z * (\sigma)/(√(n)))`

`X' = 175 + (2.326 * (20)/(√(16)))`

`X' = 175 + (2.326 * 5)`

`X' = 175 + 11.63`

`X' =186.63`

The boundary of the critical region is 186.63