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