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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.

A

Exactly normal.

Mean = $-2.68$

Standard deviation = $1.08$

B

Approximately normal.

Mean = $-2.68$

Standard deviation = $3.72$

C

Approximately normal.

Mean = $-2.68$

Standard deviation = $1.16$

D

Shape unable to be determined.

Mean = $-2.68$

Standard deviation = $1.16$

E

Shape unable to be determined.

Mean = $-2.68$

Standard deviation = $3.72$