A recent article in USA Today reported that a job awaits only one in three new college graduates. The major reasons given were an overabundance of college graduates and a weak economy. A survey of 200 recent graduates from your school revealed that 80 students had jobs.
(A) At the .01 significance level, can we conclude that a larger proportion of students at your school have jobs?

We see that the p value is so we can conclude that we have enough evidence to FAIL to reject the null hypothesis, and we can said that at 1% of significance the proportion of students with jobs is not significantly higher than 1/3 or 0.33

Step-by-step explanation:

Data given and notation

n=200 represent the random sample taken

X=80 represent the number of students with jobs

estimated proportion of students with jobs

is the value that we want to test

represent the significance level

z would represent the statistic (variable of interest)

represent the p value (variable of interest)  

Hypothesis test

We need to conduct a hypothesis in order to test the claim that the true proportion of students with job is higher than 0.33 or 1/3.:  

Null hypothesis:  

Alternative hypothesis:  

When we conduct a proportion test we need to use the z statistic, and the is given by:  

(1)  

Calculate the statistic  

Since we have all the info requires we can replace in formula (1) like this:  

Statistical decision  

The significance level provided . The next step would be calculate the p value for this test.  

Since is a right tailed test the p value would be:  

We see that the p value is so we can conclude that we have enough evidence to FAIL to reject the null hypothesis, and we can said that at 1% of significance the proportion of students with jobs is not significantly higher than 1/3 or 0.33