Answer to Question #209099 in Statistics and Probability for necati

Question

A university advertises that 90% of the graduates from their school of science find a job within one year. Researchers want to see if this is really the case and they survey 60 graduates from this university at the end of the first year after graduation and find out that 50 of them were employed. For α=0.10, is there enough evidence to conclude that the one-year employment proportion of this university is different from the advertised 90%?

Answer 1

One proportion z-test.

Null hypothesis $H_0:p=0.9.$

Alternative hypothesis $H_a:p\ne0.9.$

Test statistic: $z=\frac{\frac{50}{60}-0.9}{\sqrt{\frac{0.9(1-0.9)}{60}}}=-1.72.$

P-value: $p=2P(Z<-1.72)=0.0854.$

Since the p-value is less than 0.10, reject the null hypothesis.

There is enough evidence to conclude that the one-year employment proportion of this university is different from the advertised 90%.