Question

Exercise 5 A soap manufacturing process is designed to produce a mean of 125 bars. A sample of 10 batches shows the following number of bars of soaps. 108 118 120 122 119 113 124 122 120 123. Use alpha 0.05 to test whether the mean number of soaps is less than 125. Show all the five steps of the hypothesis testing.

Answer 1

Solution :

n = 10

= = 118.9

s² =  (x - )² / n - 1 = 4.9318

This is the left tailed test .

The null and alternative hypothesis is

H₀ : = 125

H_a : < 125

Test statistic = t

= ( - ) / s / n

= (118.9 - 125) / 4.9318 / 10

Test statistic = -3.911

P-value = 0.0018

= 0.05

P-value <

Reject the null hypothesis .

There is sufficient evidence to conclude that the mean number of soaps is less than 125.