Question

According to a recent report. 46% of college student internships are unpaid. A recent survey of 60 college interns at a local university found that 29 had unpaid internships. Use the five-stop p-value approach to hypothesis testing and a 0.01 level of significance to determine whether the proportion of college intiems that had unpaid internships is different from 0.46. Lot be the population proportion. Determine the null hypothesis, Ho, and the alternative hypothesis. Hy Ho: H: = 0.46 0.46 What is the test statistic? ZSTAT- (Type an integer or a decimal. Round to two decimal places as needed.)

Answer 1

Given information:

n = 60, and a=29 where,

n= sample size

Ộ = 0.483333

where $\mathbf{\hat{p} }$ = observed proportion

1) Problem statement

A report states that 46% of the college student internships are unpaid. To test this claim a random sample of 60 college interns is obtained. of these 29 interns had unpaid internships. is this claim accurate? use alpha= 0.01

solutions

1)Define the null and alternative hypothesis,

let x be the population proportion

Ho: x=0.46

H : x +0.46

2)What is the test statistics?

ZSTAT = P-Po po 1-po)

Po = 0.48333

p=0.46

n = 60

0.48333 - 0.46 ZSTAT = = 0.36258895 0.36 0.46(1-0.46) 60

3)Critical value

29 = 20.01 = 20.005

Here we have 0.005 in each tail. Looking up 1 - 0.005 in our z-table, we find a critical value of 2.58. Thus, our decision rule for this two-tailed test is: If Z is less than -2.58, or greater than 2.58, reject the null hypothesis. calculate Test Statistic:

• using standard normal table

$\mathbf{ Z_{0.005}=2.58}$

• Decision-based on critical value,

here we can see our ZStat value is less than 2.58 so we are going to accept the null hypothesis.

4) find the p-value

$\mathbf{p(\hat{p}>0.4833|p=0.46)}=\mathbf{p(z>0.36)}$

$\mathbf{p(z>0.36)}\mathbf{=1-P(z<0.36)=1-0.6406=0.3594}$

• criteria to reject null hypothesis using p-value,

if p - value <a we reject the null hypothesis, i.e if p - value < 0.01 we reject the null hypothesis otherwise we accept it.

• Decision-based on P-value,

Here our p-value i.e 0.3594 > 0.01 we accept the null hypothesis.

5)Conclusion:

The proportion of college interns that had unpaid internships are not different from 0.46 i.e 46% of the college students internships are unpaid