13 13 13 points The Human Resources Department of a large ma

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13. (13 points) The Human Resources Department of a large manufacturing company wants to estimate the proportion of employees who have received CPR training. Based on a simple random sample of 150 employees, it was found that 48 have CPR training. It is desired to construct a 98% confidence interval for the proportion of all employees who have CPR training. Answer the following questions. Show your work or your calculator commands. A) (2 pts) Find the point estimate, 0, of the population proportion. B) (2 pts) Find the critical value of the confidence interval. C) (2 pts) Find the margin of error of the confidence interval. D) (3 pts) Construct a 98% confidence interval for the proportion of all employees who have CPR training. E) (4 pts) If the Human Resources Department wants to keep the margin of error at 0.04 for the 98% confidence interval, what size of sample should be taken?

Solution

p = population proportion = 48/150 = 0.32

b) confidence interval critical value = 2.33, -2.33

c) Margin of error = 2.33 s = 0.0887

(s = rt of 0.32(0.68)/150 = 0.0381)

d) Conf interval 98% = (0.32-0.0887, 0.32+0.0887)

= (0.2313,0.4087)

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2.33s = 0.04

i.e. 2.33(0.32)(0.68)/rtn = 0.04

rt n = 12.6752

n = 161.