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# Type II Error in Context

APSTAT-LKKAFV

A study on women’s weights was recently completed.

Fifteen randomly selected high school females from an urban setting were compared to $16$ randomly selected high school 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 15 126.1 10.5 2.7
Rural Weights 16 128.8 13.2 3.3

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

Estimate for difference: $-2.68$

$95\%$ CI for difference: ($-11.45, 6.09$)

T-test of difference = $0$ (vs. not =): T-value = $-0.63$
P-value = $0.537$
DF = $28$

A type II error in the context of this study would involve

A

Implying there is no difference in urban versus rural weights, when really there is a difference.

B

Implying there is a difference in urban versus rural weights, when really there is no difference.

C

Implying the difference between urban and rural weights is $2.68$ pounds, when in fact it is more.

D

Implying the difference between urban and rural weights is $2.68$ pounds, when in fact it is less.

E

Implying there is no difference in urban versus rural weights, when in fact there really is no difference.