Consider college officals in admission, registration,counselling, financial aid,

Question

Consider college officals in admission, registration,counselling, financial aid, campus ministry, food service, and soon. How much money do these people make each year? Suppose you readin your local newspaper that 45 officials in student servicesearned an average of _ = $50,340 each year(Refernce: Chronicle ofHighereducation).                                                      x a. assume that = $16,920 for salaries of collegeofficials in student services. Find a 90% confidence interval forthe population mean salary of such personnel. What is the margin oferror? b. Assume that = $10,780 for salaries of collegeofficials in student services. Find a 90% confidence interval forthe population mean salary of such personnel. What is the margin oferror? c. Assume that = $4830 for salaries of collegeofficials in student services. Find a 90% confidence interval forthe population mean salary of such personnel. What is the margin oferror? d. Compare the margins of error for parts a and c. As thestandard deviation decreases, does the margin of errordecrease? e. Compare the lengths of the confidence intervals for parts athrough c. As the standard deviation decreases, does the length ofa 90% confidence interval decrease?
                                            Consider college officals in admission, registration,counselling, financial aid, campus ministry, food service, and soon. How much money do these people make each year? Suppose you readin your local newspaper that 45 officials in student servicesearned an average of _ = $50,340 each year(Refernce: Chronicle ofHighereducation).                                                      x a. assume that = $16,920 for salaries of collegeofficials in student services. Find a 90% confidence interval forthe population mean salary of such personnel. What is the margin oferror? b. Assume that = $10,780 for salaries of collegeofficials in student services. Find a 90% confidence interval forthe population mean salary of such personnel. What is the margin oferror? c. Assume that = $4830 for salaries of collegeofficials in student services. Find a 90% confidence interval forthe population mean salary of such personnel. What is the margin oferror? d. Compare the margins of error for parts a and c. As thestandard deviation decreases, does the margin of errordecrease? e. Compare the lengths of the confidence intervals for parts athrough c. As the standard deviation decreases, does the length ofa 90% confidence interval decrease?
                                           

Explanation / Answer

given that the mean earning ,Xbar =$ 50340 and the sample size, n = 45 a)given that standard deviation, =$16920 then the 90% confidence interval for the population meansalary is                           50340 ± 1.645 * (16920/45)                  50340 ± 1.645 (2522.29)                    50340±4149.16                 ( 46190 , 54489.16) the margin of error, Z/2*(/n) =1.645 * (16920/45)                                                   =4149.16 b)   standard deviation, =$10780 then the 90% confidence interval for the population meansalary is                           50340 ± 1.645 * (10780/45)                  50340 ± 1.645 (1606.99)                    50340±4348.55                 ( 45991.45 , 54688.55) the margin of error, Z/2*(/n) =1.645 * (10780/45)                                                   =4348.55 c)standard deviation, =$4830 then the 90% confidence interval for the population meansalary is                           50340 ± 1.645 * (4830/45)                  50340 ± 1.645 (720)                    50340±1184.423                 ( 49155.58 , 51524.423) the margin of error, Z/2*(/n) =1.645 * (4830/45)                                                   =184.423 d) comapring a and c, by decreasing the standard deviation, the width of theconfidence interval has increased and the margin of error has decreased

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