Moderate# T-Sampling Distribution

APSTAT-JDVTDP

A study on women’s weights was recently completed.

Twenty randomly selected high school females from an urban setting were compared to $21$ randomly selected females from a rural setting. The results are below:

**Two-Sample $T$ for Urban Weights vs. Rural Weights**

N | Mean | StDev | SE Mean | |
---|---|---|---|---|

Urban Weights | 20 | 126.1 | 10.5 | 2.35 |

Rural Weights | 21 | 128.8 | 13.2 | 2.88 |

$\text{Difference} = \mu \text{(Urban Weights)} - \mu \text{(Rural Weights)}$

$\text{Estimate for difference}: -2.68$

$95\% \text{ Confidence Interval for difference}: (-10.22, 4.824)$

$T\text{-test of difference} = 0\ (\text{vs. not equal to}):\ T\text{-value} = -0.73\ P\text{-value} = 0.472 \text{ DF} = 37.8$

Describe the sampling distribution of the difference between urban and rural weights.