Question

a.   Test if the proportion of unemployed non-science male graduates is 5 percent less than the proportion of unemployed science male graduates at 10 percent significance level.

 

i)            Specify the competing hypotheses of the test           (2 Marks)

ii)           Calculate the value of the relevant test statistic         (4 Marks)

    

Answer 1

Solution:

$H_0:p=5\% \\H_1:p<5\%$

$\hat p, n$ are not given, assume $n = 10,\hat p=4.5\%=0.045$

Then, test statistic $=\dfrac{\hat p-p}{\sqrt{\dfrac{p(1-p)}{n}}}$

$=\dfrac{0.045-0.05}{\sqrt{\dfrac{0.05(1-0.05)}{10}}}=-0.072$

Critical value for 10% significance level for one-tailed test, is 1.28

We get, -0.072 < 1.28

We have not sufficient evidence to reject $H_0$.

Thus, $p=5\%$