Dottie Kleman is the Cookie Lady. She bakes and sells cookies at locations in th

Question

Dottie Kleman is the Cookie Lady. She bakes and sells cookies at locations in the Philadelphia area. Ms. Kleman is concerned about absenteeism among her workers. The information below reports the number of days absent for a sample of 10 workers during the last two-week pay period. 4 2 2 2 2 2 2 1 0 3 (a) (3 points) Determine the mean and the standard deviation of the sample. Sample Mean: X¯ = . Standard deviation of the sample: s = (b) (3 points) What is the population mean? What is the best estimate of that value? Population Mean: µ = . Best estimation (c) (3 points) Develop a 95% confidence interval for the population mean. Assume that the population distribution is normal. (d) (3 points) Explain why the t distribution is used as a part of the confidence interval. (e) (3 points) Is it reasonable to conclude that the typical worker does not miss any days during a pay period?

Explanation / Answer

(a)The mean is: (4+2+...+3)/10=2

The standard deviation is:

root over(xi-xbar)^2/n-1

=1.054

b)The best pont estimate of population mean is sample mean=2

c)

The estimated standard error of mean is:

Sm=root over s^2/n

=rootover 1.054^2/10

=0.33

The 95% Confidence interval is:

x bar+/-t(0.05,9)*Sm

=2+/-2.262*0.33

=(1.25,2.74)

d)Since the ppulation standard deviation is not given the t distribution is used as a part of the confidence interval.

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