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 Upper H Subscript 0 Baseline colon mu ⁢ equals 175 millimeters versus Upper H Subscript 1 Baseline colon mu ⁢ greater-than 175 millimeters, using the results of n equals 4 samples. Calculate the P-value if the observed statistic is 182 Round your answer to four decimal places

Answer 1

Solution :

The null and alternative hypothesis is

H0 :   = 175

H1 : > 175

= 182

= 20

n = 4

Test statistic = z =

= ( - ) / / n

= (182 - 175) / 20 / 4

Test statistic = z = 0.70

This is the right tailed test,

P(Z > 0.70) = 1-P (Z < 0.70) = 1 - 7580

P-value = 0.2420