Question

Are women’s feet getting bigger? Retailers in the last 20 years have had to increase their stock of larger sizes. WalMart Stores, Inc., and Payless ShoeSource, Inc., have been aggressive in stocking larger sizes, and Nordstrom’s reports that its larger sizes typically sell out first. Assuming equal variances, at α = .025, do these random shoe size samples of 12 randomly chosen women in each age group show that women’s shoe sizes have increased?

Born in 1980:	8	7.5	8.5	8.5	8	7.5	9.5	7.5	8	8	8.5	9
Born in 1960:	8.5	7.5	8	8	7.5	7.5	7.5	8	7	8	7	8

(a) Choose the appropriate hypotheses assuming equal variances at α = .025.

1. H₀: μ₁₉₆₀ – μ₁₉₈₀ ≥ 0 vs. H₁: μ₁₉₆₀ – μ₁₉₈₀ < 0. Reject H₀ if t_calc < –2.074.
2. H₀: μ₁₉₆₀ – μ₁₉₈₀ ≤ 0 vs. H₁: μ₁₉₆₀ – μ₁₉₈₀ > 0. Reject H₀ if t_calc > –2.074.
3. H₀: μ₁₉₆₀ – μ₁₉₈₀ ≥0 vs. H₁: μ₁₉₆₀ – μ₁₉₈₀ < 0. Reject H₀ if t_calc < 2.074.
4. H₀: μ₁₉₆₀ – μ₁₉₈₀ ≤0 vs. H₁: μ₁₉₆₀ – μ₁₉₈₀ > 0. Reject H₀ if t_calc < 2.074.

• a

• b

• c

• d

(b) The average shoe size of women has increased.

• True

• False

Answer 1

Solution: ot Calcutate data D ean Mean ( E 8 .5 Meon 208 Sd O 620 data 1960 C alcalate mean the Neon O4SD n on)S(n-1)s SP (IL-D0-62)Ct2-1)(0 450) Sp t2-2 sp O.54 2 tatistics!- Test Sp S.208-.F08 O 22127 dt t2+12 2E 22. nitn22

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