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

Step-by-step 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 :  $\hat{p}=\dfrac{295}{390}=0.7564$

Test statistic for proportion :

$z=\dfrac{\hat{p}-p}{\sqrt{\dfrac{p(1-p)}{n}}}$

Substitute the values , we get

$z=\dfrac{0.7564-0.80}{\sqrt{\dfrac{0.80(1-0.80)}{ 390}}}$

$z=\dfrac{-0.0436}{\sqrt{0.000410256410256}}$

$z=-2.15257752474\approx-2.15$

Hence, the value of test statistic = -2.15

Correct option is c. -2.15 .