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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

Difference = $\mu$ (Urban Weights) - $\mu$ (Rural Weights)

Estimate for difference: $-2.68$

$95\%$ CI for difference: ($-10.22, 4.824$)

T-test of difference = $0$ (vs. not =): T-value = $-0.73$ P-value = $0.472$ 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