Answer:
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