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?

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1 23 4 5 6 7 8 910 11 12 Daughter 8 8 7.5 8 9 9 8.5 9 9 8 78 Mother 7 7 7.5 8 8.5 8.5 7.5 75 6 8 77