Question

Are women's feet getting bigger? retailers in the last 20 years have had to increase their stock of larger sizes. wal-mart 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 click here for the excel data file (a) choose the appropriate hypotheses assuming equal variances at α = .025.

a. h0: μ1960 – μ1980 ≥ 0 vs. h1: μ1960 – μ1980 < 0. reject h0 if tcalc < –2.074.
b. h0: μ1960 – μ1980 ≤ 0 vs. h1: μ1960 – μ1980 > 0. reject h0 if tcalc > –2.074.
c. h0: μ1960 – μ1980 ≥0 vs. h1: μ1960 – μ1980 < 0. reject h0 if tcalc < 2.074.
d. h0: μ1960 – μ1980 ≤0 vs. h1: μ1960 – μ1980 > 0. reject h0 if tcalc < 2.074. a b c d (b) the average shoe size of women has increased. false true

Answer 1

Since it is assumed that the average feet sizes in the 1960s are equal or greater than the average feet sizes in the 1980s, the following hypotheses are chosen:
(a) h0: μ1960 – μ1980 ≥ 0 vs. h1: μ1960 – μ1980 < 0. reject h0 if t calc < –2.074

After applying a paired t-test for the given data, at α = .025 there is a difference between the two methods. Therefore, (b) the average shoe size of women has increased.