Question

Increasing numbers of businesses are offering child-care benefits for their workers. However, one union claims that 90% of firms in the manufacturing sector still do not offer any child-care benefits to their workers. A random sample of 370 manufacturing firms is selected, and only 34 of them offer child-care benefits. Suppose the p-value for this test was reported to be p = 0.1071. State the conclusion of interest to the union. Use α = 0.05.

Hypothesis Testing: __

Answer 1

At the 5% significance level and with a p-value of 0.1071, there is insufficient evidence to support the union's claim that 90% of manufacturing firms do not offer child-care benefits, leading to the decision to not reject the null hypothesis.

Step-by-step explanation:

Using a significance level of alpha = 0.05, and given the p-value = 0.1071, the conclusion for the hypothesis test is to do not reject the null hypothesis. Because the p-value is higher than the significance level, there is insufficient evidence to support the union's claim that 90% of firms in the manufacturing sector do not offer child-care benefits to their workers.

Another way to state the conclusion is that, at the 5 percent significance level, the union's claim is not substantiated by the sample data. Hence, there might be less than 90% of manufacturing firms without child-care benefits, however, the evidence from this specific sample of 370 firms is inconclusive to definitively support the claim due to the p-value being higher than the chosen alpha.