In: Statistics and Probability
2. Wal-Mart Stores, Inc., and Payless ShoeSource, Inc., have been aggressive in stocking larger size women shoes and Nordstrom reports that its larger sizes typically sell out first. The following is a random sample of shoe sizes for twelve mothers and their daughters who shop at Nordstrom. Does the data support the Management assertion that the demand for larger show sizes has increased. Use 0.025 significance level.
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 |
8.5 |
6 |
7.5 |
7.5 |
7.5 |
8 |
9 |
8 |
7 |
C.
t-Test: Two-Sample Assuming Equal Variances | ||
Daughter | Mother | |
Mean | 8.25 | 7.541666667 |
Variance | 0.431818182 | 0.611742424 |
Observations | 12 | 12 |
Pooled Variance | 0.521780303 | |
Hypothesized Mean Difference | 0 | |
df | 22 | |
t Stat | 2.401980429 | |
P(T<=t) one-tail | 0.012594278 | |
t Critical one-tail | 1.717144374 | |
P(T<=t) two-tail | 0.025188555 | |
t Critical two-tail | 2.073873068 |
Here Ts > 1.96,
We do reject Null Hypothesis.