1) To find the effect of a recent policy change on employee morale, a large corporation decides to conduct an opinion survey, asking N randomly selected employees whether they are satisfied or not (i.e. yes/no) with the new policy.

a. How many employees must be sampled to guarantee a sampling error (95% confidence interval) within +/ 3%? (Hint: Recall class discussion of sample size to meet error margin requirements for unknown proportions.)

b. A survey is conducted, using the value of N chosen in part a. This survey reveals that 62.5% of the sampled employees are satisfied with the new policy. What is the 95% confidence interval for p, the proportion of all company employees that are satisfied with the new policy? What is the 99% confidence interval for p?

c. Does the 95% confidence interval suggest that a majority of employees are satisfied with the policy?

2. During the electoral campaign, the mayor comes under criticism that City Hall and local public utilities are discriminating against Asians in the hiring process (that Asians are less likely to be hired than other races/ethnicities). You find that the proportion of Asians employed by local authorities is 7%, in a random sample of 300 public employees, while they represent 10% of the general population.

a. Conduct a hypothesis tests of whether City Hall is discriminating against Asians for = 0.02. Clearly state the null and alternative hypotheses and the conclusion of your test.

b. What is the p-value of your test?

c. In the context of this problem what is Type I error and in describe the cost of making a Type I error ?

d. In the context of this problem what is Type II error and describe the cost of making a Type II error ?

e. Conduct a hypothesis tests of whether City Hall has fair hiring practices for = 0.02. Clearly state the null and alternative hypotheses and the conclusion of your test as well as the p-value for the test.