Would we be justified in assuming that we have equal variances for the hypothesis test reported below? (This two-sample t-test examines the mean number of alcoholic drinks consumed each week by whether or not the respondent smokes or uses tobacco products.) Two-sample t test with equal variances Group No Yes combined Obs 177 34 211 Mean Ha: diff < @ Pr(Tt) = 0.0000 7.073446 .6875901 14.94118 2.369947 8.341232 diff diff mean (No) - mean(Yes) Ho: diffe -7.86773 Std. Err. Std. Dev. (95% Conf. Intervall 9.147791 5.716464 8.430429 13.81905 10.11948 19.76287 7172541 10.41872 1.878282 6.927291 Ha: diff != e Pr(IT] It) 0.0000 -11.57054 -4.164923 degrees of freedon 9.755173 t-4.1888 No, because the standard deviations are not the same Yes, because the product of three times .69 is less than 2.37 Yes, because the product of three times 9.15 is greater than 13.82 No, because the standard errors are not equal 209 Ha: diff Pr(Tt) 1.0000

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I know that the answer to this is C (Yes, because the product of three times 9.15 is greater than 13.82), but I am confused as to where the x 3 comes from?
Would we be justified in assuming that we have equal variances for the hypothesis test reported below? (This
two-sample t-test examines the mean number of alcoholic drinks consumed each week by whether or not the
respondent smokes or uses tobacco products.)
Two-sample t test with equal variances
Group
No
Yes
combined
diff
Obs
177
34
211
Mean
Ha: diffe
Pr(Tt) = 0.0000
7.073446
14.94118
8.341232
-7.86773
diff mean (No) - mean (Yes)
Ho: diffe
Std. Err..
Std. Dev. (95% Conf. Intervall
.6875901 9.147791 5.716464 8.430429
2.369947 13.81905 10.11948 19.76287
9.755173
-11.57054 -4.164923
.7172541 10.41872
1.878282
6.927291
Ha: diff !=0
Pr|TI|t|) = 0.0000
t-4.1888
degrees of freedom -
Ha: diff > @
Pr(Tt) 1.0000
No, because the standard deviations are not the same
Yes, because the product of three times .69 is less than 2.37
Yes, because the product of three times 9.15 is greater than 13.82
No, because the standard errors are not equal
209
M
Transcribed Image Text:Would we be justified in assuming that we have equal variances for the hypothesis test reported below? (This two-sample t-test examines the mean number of alcoholic drinks consumed each week by whether or not the respondent smokes or uses tobacco products.) Two-sample t test with equal variances Group No Yes combined diff Obs 177 34 211 Mean Ha: diffe Pr(Tt) = 0.0000 7.073446 14.94118 8.341232 -7.86773 diff mean (No) - mean (Yes) Ho: diffe Std. Err.. Std. Dev. (95% Conf. Intervall .6875901 9.147791 5.716464 8.430429 2.369947 13.81905 10.11948 19.76287 9.755173 -11.57054 -4.164923 .7172541 10.41872 1.878282 6.927291 Ha: diff !=0 Pr|TI|t|) = 0.0000 t-4.1888 degrees of freedom - Ha: diff > @ Pr(Tt) 1.0000 No, because the standard deviations are not the same Yes, because the product of three times .69 is less than 2.37 Yes, because the product of three times 9.15 is greater than 13.82 No, because the standard errors are not equal 209 M
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