The head of the statistics department in a certain university believes that 70% of the department's graduate assistantships are given to international students. A random sample of 50 graduate assistants is taken.
a. Assume that the chairman is correct and p = 0.70. What is the sampling distribution of the sample proportion $\hat { p }$ . Explain.
b. Find the expected value and the standard error of the sampling distribution of $\hat { p }$ .
c. What is the probability that the sample proportion $\hat { p }$ will be between 0.65 and 0.73?
d. What is the probability that the sample proportion $\hat { p }$ will be within ±0.05 of the population proportion p?

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The Answer of The head of the statistics department in a certain university believes that 70% of the department's graduate assistantships are given to international students. A random sample of 50 graduate assistants is taken.
a. Assume that the chairman is correct and p = 0.70. What is the sampling distribution of the sample proportion $\hat { p }$ . Explain.
b. Find the expected value and the standard error of the sampling distribution of $\hat { p }$ .
c. What is the probability that the sample proportion $\hat { p }$ will be between 0.65 and 0.73?
d. What is the probability that the sample proportion $\hat { p }$ will be within ±0.05 of the population proportion p?

The Head of the Statistics Department in a Certain University p^\hat { p }p^​

The Head of the Statistics Department in a Certain University $\hat { p }$