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# Sampling to Derive Meaningful Statistics

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1. Given the following population data: 1,2,4,5,8,9,12, and the lists of all samples of size 2 and 5:

Samples of n = 2
xbar Samples of
n = 5
xbar
1,2 1.5 For population 1,2,4,5,8 4
1,4 2.5 s = ? 1,2,4,5,9 4.2
1,5 3 m = ? 1,2,4,5,12 4.8
1,8 4.5 1,2,4,8,9 4.8
1,9 5 1,2,4,8,12 5.4
1,12 6.5 1,2,4,9,12 5.6
2,4 3 For n = 2 1,2,5,8,9 5
2,5 3.5 sxbar = ? 1,2,5,8,12 5.6
2,8 5 mxbar = ? 1,2,5,9,12 5.8
2,9 5.5 1,2,8,9,12 6.4
2,12 7 1,4,5,8,9 5.4
4,5 4.5 1,4,5,8,12 6
4,8 6 For n = 5 1,4,5,9,12 6.2
4,9 6.5 sxbar = ? 1,4,8,9,12 6.8
4,12 8 mxbar = ? 1,5,8,9,12 7
5,8 6.5 2,4,5,8,9 5.6
5,9 7 2,4,5,8,12 6.2
5,12 8.5 2,4,5,9,12 6.4
8,9 8.5 2,5,8,9,12 7.2
8,12 10 4,5,8,9,12 7.6
9,12 10.5 2,4,8,9,12 7

a) Use Excel to find the six ? values above.

b) Consider the three values of mean and the three values of standard deviation in a). Verify (mathematically) that the Central Limit Theorem applies using the formulas:
µ = µxbar and sxbar = s / vn

2.
Dunkin Donuts advertises that a dozen of their donuts weighs about 43 oz. A certain baker has figured out that she can stay out of trouble with her manager if each donut weighs about 3.6 oz. To test her donut-making process, she randomly selects thirty-one donuts after baking and weighs them. The average of the sample is 3.504 oz with s = 0.109 oz. Construct a 95% confidence interval for the true population mean of donut weights, and then explain whether or not she will be in trouble.
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