Question 179742
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.