Question 1. A company offers 60 of its employees a free training program. 40 employees choose to participate in the training program. Let p be the probability that an employee will participate in the training program in the population.

Compute the test statistic for the following hypothesis test:

H₀ : p = 0.5

H₁ : p != 0.5

Question 2. Using the same information as in Question 1., which of the following statements is true?

(a)Under the Null hypothesis, the test statistic is a standard normal random variable. We reject the Null hypothesis at = 0.05.

(b)Under the Alternative hypothesis, the test statistic is a standard normal random variable. We reject the Null hypothesis at = 0.05.

(c)Under the Null hypothesis, the test statistic follows the t-distribution. We reject the Null hypothesis at = 0.01.

(d)Under the Null hypothesis, the test statistic follows the t-distribution. We reject the Null hypothesis at = 0.05.

Question 3. Using the same information as in Question 1., compute the test statistic for the following hypothesis test

H₀ : p 0.5

H₁ : p > 0.5

Question 4. Consider the hypothesis test in Question 3., which of the following statements is true?

(a)We reject the Null hypothesis at = 0.01

(b)We do not reject the Null hypothesis at = 0.01

(c) The p-value of the test is smaller than = 0.01

(d) (a) and (c)

Question 5. Consider the two hypothesis tests in Question 1. and Question 3.. For the same level, we will reject the Null hypothesis for both tests, or we will not reject the Null hypothesis for both tests. True or False?

(a)True

(b)False