Answer to Question #219451 in Statistics and Probability for June

Question

2. A research states that 28% of college degrees are from engineering courses. A researcher doesn't
believe that this is correct. A sample of 1.000 graduates was used and it was found out that 295 have
finished engineering courses. Test the claim if it has increased at a = 0,10 level. What is the correct
null hypothesis?

Answer 1

$H_0:P=0.28$

$H_1:P>0.28$

The correct Null hypothesis is $H_0:P=0.28$. 28% of college degrees are from engineering courses as stated by a research.

$x=295$

$n=1000$

$\hat P=0.295$

$z=\frac{\hat P-P}{\sqrt{\frac{P(1-P)}{n}}}$

$z=\frac{0.295-0.28}{\sqrt{\frac{0.28\times(1-0.28)}{1000}}}$

$=1.056$

$CV=Z_{0.1}=1.282$

Since the test statistics 1.056 is less that the critical value, 1.282, we fail to reject the null hypothesis. There is no sufficient evidence to support the claim that engineering courses proportion has increased.