Question

Increasing numbers of businesses are offering child-care benefits for their workers. However, one union claims that fewer than 80% of firms in the manufacturing sector offer child-care benefits and performs a hypothesis test with a-0.05. A random sample of 390 manufacturing firms is selected and 295 of them offered child-care benefits. Symbolically, the null and alternative hypothesis are as follows: Hop -0.80 and Hap<0.80 What value of the 2-statistic should he report? Round your standard error to four decimal places for calculations.

a. -0.0125
b. 0.0125
c. -2.15
d. 2.15

Answer 1

Answer: c. -2.15

Explanation:

As per given we have:

Null hypothesis :
`H_(a): p\geq0.80`

Alternative hypothesis :
`H_(a): p<0.80`

let p be the proportion of firms in the manufacturing sector offer child-care benefits

A random sample of 390 manufacturing firms is selected and 295 of them offered child-care benefits.

sample size : n= 390

sample proportion :
`\hat{p}=(295)/(390)=0.7564`

Test statistic for proportion :

`z=\frac{\hat{p}-p}{\sqrt{(p(1-p))/(n)}}`

Substitute the values , we get

`z=\frac{0.7564-0.80}{\sqrt{(0.80(1-0.80))/( 390)}}`

`z=(-0.0436)/(√(0.000410256410256))`

`z=-2.15257752474\approx-2.15`

Hence, the value of test statistic = -2.15

Correct option is c. -2.15 .