Null and alternative hypotheses set up

Question

In a survey of 1120 new college graduates 281 had a professional job on graduation day. One year ago the proportion of graduates with a professional job on graduation day was 24%. The setup of the null and alternative hypotheses to test whether there is sufficient evidence to conclude that the proportion of graduates with a professional job is higher now than it was one year ago is:

 

a) H_o: p=.24  vs.  H₁: p<.24

b) H_o: p=.24   vs.  H₁: p≠.24

c) H₀: p=.24   vs.  H₁: p>.24

d) Ho: p=.25    vs.  H₁: p<.25

e) Ho: p=.25    vs.  H₁: p>.24

Answer 1

The null hypothesis is that there is no change from last year, that is H₀: p=.24  

The alternative hypothesis is that p is higher now than it was one year ago, that is H₁: p>.24 

Answer 2

You're testing two proportions to determine whether they are different. This year, the proportion of those graduates who had jobs is 281/1120 or 0.25. Last year it was 0.24.

 

The null hypothesis says that 0.25 is the same as 0.24.

 

The alternative hypothesis says that 0.25 is different from 0.24.

 

You can use a chi square test. You'll get a Pearson chi^2 value with one degree of freedom and a probability. If the probability is less than your cutoff, like less than 0.05, then you can reject the null hypothesis.

 

You need last year's numbers though, not just a proportion. If the previous year's numbers are too few, then the chi square test is not appropriate.