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(4-5) The chairman of the statistics department in a certain college believes that 70% of the...

(4-5) The chairman of the statistics department in a certain college believes that 70% of the department's graduate assistantships are given to international students. A random sample of 50 graduate assistants is taken.

4. Find the expected value and the standard error of the sampling distribution of  .

5. What is the probability that the sample proportion  is between 0.65 and 0.73?

(6-9) Suppose that the starting salaries of female math professors have a positively skewed distribution with mean of $56,000 and a standard deviation of $12,000. The starting salaries of male math professors are positively skewed with a mean of $50,000 and a standard deviation of $10,000. A random sample of 50 female math professors and a random sample of 40 male math professors are selected.

6. What is the sampling distribution of the sample mean difference ? 7. Find the expected value of the sample mean difference .
8. Find the standard error of the sample mean difference .

9. What is the probability that the sample mean salary of male math professors will not exceed that of the female math professors?

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