Question

The National Science Foundation, in a survey of 2,237 engineering graduate students who earned their PhD degrees, found that 607 were U.S. citizens; the majority (1,630) of the PhD degrees were awarded to foreign nationals. Conduct a test to determine whether the true proportion of engineering PhD degrees awarded to foreign nationals exceeds .5. Use α = .01.

Please follow these steps:

1. State the null and alternate hypothesis.

2. significance level used.

3. Test statistic.

4. p-value.

5. Decision.

6. Conclusion.

Answer 1

To test :

Test statistic :

where ,

The value of the test statistic :

We reject the null hypothesis if the

Now ,

Hence we reject the null hypothesis or H₀ .

Thus we have sufficient evidence to support the claim that  the true proportion of engineering PhD degrees awarded to foreign nationals exceeds 0.5 .