Question

Increasing values of businesses are offering opportunities such as child care benefits for their employees. But, one local union states that more than 80% of firms in the producing sector still don’t offer value services such as child care benefits. A randomized sample was done of 390 manufacturing firms, and they were asked if they were offered child care benefits. Assume p-value for this test is p=0.1112. Alpha=0.10

Ho:

H1:

Test statistic:

Alpha:

P-value:

Conclusion:

Also explain the type I error and type II error for this problem.

Answer 1

Solution:

The null and alternative hypotheses for this test are given as below:

H0: p = 0.80

H1: p > 0.80

This is an upper tailed or right tailed (one tailed) test.

Test statistic: Z = 1.22

(by using z-table)

[Find the inverse value for the probability 1 – 0.1112]

Alpha: α = 0.10

P-value = 0.1112

Conclusion:

Since P-value > α = 0.10, we do not reject the null hypothesis

So, there is no sufficient evidence to conclude that more than 80% of firms in the producing sector still don’t offer value services such as child care benefits.

Type I error occurred when we conclude that more than 80% of firms in the producing sector still don’t offer value services such as child care benefits, however, in fact, it is not more than 80%.

Type II error occurred when we conclude that less than or equal to 80% of firms in the producing sector still don’t offer value services such as child care benefits, however, in fact, it is more than 80%.