4. Sales personnel for Skillings Distributors are required to submit weekly 4. S

Question

4. Sales personnel for Skillings Distributors are required to submit weekly 4. Sales personnel for Skilings Distributors are required to submit weekly reports listing the customer contacts made during the week. A sample of weekly contact reports showed a mean of 22.4 customer contacts per week for the sales personnel. The sample standard deviation was 5 contacts. 61 a. what is the 95% confidence interval for the population mean? b. what is the 92% confidence interval for the population mean? c. What happened to your confidence interval when you changed your level of confidence, everything else remaining equal?

Explanation / Answer

4.) Sample size is 61. Hence, we can use z statistic.

Mean = 22.4

Standard Deviation = 5

Standard error = 5/61 = 0.64

z value for 95% confidence level = 1.96

z value for 92% confidence level = 1.75

a.) 95% confidence interval = [22.4+0.64*1.96, 22.4-0.64*1.96]

= [23.65, 21.14]

b.) 92% confidence interval = [22.4+0.64*1.75, 22.4-0.64*1.75]

= [23.52, 21.27]

c.) Cofindence interval marginally shrank.

5.) Z = 1.96

Z = 1.5 / (17/n)

1.96 = 1.5 / (17/n)

n = 494

6.)

a.) Mean = p

SD of proportions = p(1-p)/n

b.) t = 0.03/(0.76(1-0.76)/400)

= 1.40

P(t=1.40) = 0.1622

c.) t = 0.03/(0.76(1-0.76)/750)

= 1.92

P(t=1.40) = 0.055

  

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