Question 179742: 10.24 - 10.24 Below is a random sample of shoe sizes for 12 mothers and their daughters. (a) At α = .01, does this sample show that women’s shoe sizes have increased? State your hypotheses and show all steps clearly. (b) Is the decision close? (c) Are you convinced? (d) Why might shoe sizes change
over time? (See The Wall Street Journal, July 17, 2004.) Shoe Size 2
1 2 3 4 5 6 7 8 9 10 11 12
Daughter 8 8 7.5 8 9 9 8.5 9 9 8 7 8
Mother 7 7 7.5 8 8.5 8.5 7.5 7.5 6 8 7 7
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! Below is a random sample of shoe sizes for 12 mothers and their daughters.
Daughter 8 8 7.5 8 9 9 8.5 9 9 8 7 8
d-bar = 8.25 ; s = 0.657
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Mother 7 7 7.5 8 8.5 8.5 7.5 7.5 6 8 7 7
m-bar = 7.46 ; s = 0.721
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(a) At α = .01, does this sample show that women’s shoe sizes have increased? State your hypotheses and show all steps clearly.
Ho: ud-um = 0
Ha: ud-um < 0 (this for a right-tail test; you could reverse the inequality
and make a left tail test)
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Critical Value: z = 2.326...
Test statistic: z(8.25-7.46) = (0.79)/sqrt[(0.657)^2/12 + (0.721)^2/12] = 2.81
p-value: P(z>2.81) = 0.0025
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Conclusion: Since p-value < 1%, reject Ho.
daughter's sizes are greater than mother's sizes
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(b) Is the decision close?
No. Less than (1/4) of 1% of test results could have provided stronger
evidence for rejecting Ho.
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(c) Are you convinced?
Yes
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(d) Why might shoe sizes change over time?
They don't; foot sizes change.
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Cheers,
Stan H.
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