A company knows from past experience that 50% of its employees have chosen to participate in a voluntary pre-tax savings plan. The company makes some changes to the plan and conducts a telephone...

A company knows from past experience that 50% of its employees have chosen to

participate in a voluntary pre-tax savings plan. The company makes some changes

to the plan and conducts a telephone survey of 100 randomly selected employees

to ask if they will still participate in the plan with the new changes. 43 out of the 100

employees surveyed say that they will participate in the plan. The company wants

to test the null hypothesis that the percentage of employees who will participate in

the plan is unchanged from past years (50% of employees).



(a) Carry out all the steps of the z test to evaluate the whether the percentage of

employees who will participate in the plan is unchanged from past years. You

should show the null and alternative hypothesis, the box model, z-statistic, p-value

and state your conclusion in the context of the original problem.

b) How does your conclusion change if our sample size had 400 instead of 100

employees, but still had 43% participating in the plan.