Your company sells exercise clothing and equipment on the Internet. To design th

Question

Your company sells exercise clothing and equipment on the Internet. To design the clothing, you collect data on the physical characteristics of your different types of customers. Below are the weights (in pounds) for a sample of 11 male runners. Assume that these runners can be viewed as a random sample from a normally distributed population of your potential male customers.

customer1 weight 131.82

customer2 weight 141.34

customer3 weight 125.55

customer4 weight 157.46

customer5 weight 150.96

customer6 weight 136.88

customer7 weight 164.20

customer8 weight 144.04

customer9 weight 152.06

customer10 weight 168.14

customer11 weight 147.58

(a) Determine the sample mean and sample standard deviation for this data.

(b) Determine a 95% confidence interval for , the mean weight of all male customers of your company.

(c) Determine a 99% confidence interval for .

(d) Suppose, somehow, the actual population standard deviation became known to your company and it is taken as = 12.20 pounds. Redo part (b) and part (c) under this assumption.

(e) Suppose the weights of the male runners listed above are registered in kilograms as opposed to pounds. Recall that 1 kilogram = 2.2 pounds. So, the first entry in the above sample would now be listed as 131.82 / 2.2 = 59.918. Determine how this would affect your confidence intervals.

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Explanation / Answer

a. Here mean=147.28 and sd=13.14

b. t table value for 95% CI is 2.228

So E=t*sd/sqrt(n)=8.83

Hence CI=mean+/-E=(138.45,156.11)

c. Similarly for t=3.169 at 99%

E=12.56

Hence CI=(134.72,159.84)

d. For sd=12.20, SE=sd/sqrt(n)=3.68

So E for 95%=8.20, so CI=(139.08,155.48)

and E for 99% =11.66, hence ci=(135.62,158.94)

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