Question

A recent article reported that a job awaits only one in three new college graduates. (1 in 3 means the proportion is .333) A survey of 200 recent graduates revealed that 80 graduates had jobs. At the .02 significance level, we will conduct a hypothesis test to determine if we can conclude if a larger proportion of graduates have jobs than previously reported.

a.What will be the value of our critical value?
b.What will be the value of our test statistic?
c.can we conclude that a larger proportion of graduates have jobs than reported in the article?

Answer 1

a)
`2.05`

b)
`z = 2.01`

c) No, we cannot conclude that a larger proportion of graduates have jobs than reported in the article.

Explanation:

We are given the following in the question:

Sample size, n = 200

p = 0.333

Alpha, α = 0.02

Number of graduates had jobs , x = 80

First, we design the null and the alternate hypothesis

`H_(0): p = 0.333\\H_A: p > 0.333`

This is a one-tailed(right) test.

b) Formula:

`\hat{p} = (x)/(n) = (80)/(200) = 0.4`

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

Putting the values, we get,

a)
`z = \displaystyle\frac{0.4-0.333}{\sqrt{(0.333(1-0.333))/(200)}} = 2.01`

Now,
`z_(critical) \text{ at 0.02 level of significance } = 2.05`

c) Since, the calculated z statistics less than the critical value, we fail to reject the null hypothesis and accept it.

Thus, same proportion of graduates have jobs as compared to previously reported.

Thus, we conclude that there is not enough evidence to support the claim that a larger proportion of graduates have jobs than previously reported.