In a company made up of 30,000 employees, 6,900 (23%) are enrolled in an optional savings program. The company is considering changing the program and decides to first take a poll of 500 randomly selected employees. In this problem we will look at the sample percentage of employees who are enrolled in the program. (a) Write down all elements of the box model. (b) The average of the tickets in the box is _______ and the SD is _______. (c) Consider the percentage of employees in the sample who are enrolled in the program. What is its expected value? __________% What is its standard error? __________% (d) Use the normal approximation to calculate the chance that the percentage of employees in the sample who are enrolled in the program is between 22% and 24%. Answer: _____________% (e) How do you justify using the normal approximation in (d)? (Your answer should include the name of a theorem and one or more numerical comparisons.
In a company made up of 30,000 employees, 6,900 (23%) are enrolled in an optional savings program. The company is considering changing the program and decides to first take a poll of 500 randomly selected employees. In this problem we will look at the sample percentage of employees who are enrolled in the program.
(a) Write down all elements of the box model.
(b) The average of the tickets in the box is _______ and the SD is _______.
(c) Consider the percentage of employees in the sample who are enrolled in the program.
What is its
(d) Use the normal approximation to calculate the chance that the percentage of employees in the sample who are enrolled in the program is between 22% and 24%.
Answer: _____________%
(e) How do you justify using the normal approximation in (d)? (Your answer should include the name of a theorem and one or more numerical comparisons.
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