As part of a long-term study of individuals 65 years of age or older, sociologis

Question

As part of a long-term study of individuals 65 years of age or older, sociologists and physicians at the Wentworth Medical Center in upstate New York investigated whether geographic location had an effect on depression. Random samples of 40 individuals were selected from three geographic locations: Florida, New York, and North Carolina. Then, each was given a standardized test to measure depression (higher test scores indicate higher levels of depression). Determine if there are significant differences in the mean depression scores across the three geographic locations using a significance level of 0.01.

Select the appropriate hypotheses:

Ho:?1=?2=?3
Ha:?1??2??3

Ho:?1??2??3
Ha:?1=?2=?3

Ho:?1=?2=?3
Ha: some differences in the means

? = __

TS: f = __ (round your answer to 3 decimal places)

probability = __

Decision: fail to reject H? reject H?

Interpret: At the 0.01 level, there is/is not significant evidence to conclude there is some difference in the mean depression score/geographic location for adults 65 and older across the three geographic locations.

Which of the multiple comparisons are significant?

(a) FL vs. NY

(b) FL vs. NC

(c) NY vs. NC

(d) It is not appropriate to consider multiple comparisons

PLEASE SHOW YOUR WORK. THANK YOU.

Response statistics by factor Tukey 99% Simultaneous Confidence Intervals: Location+ n+ Mean* Std. Dev. Std. Error Florida New York North Carolina 40 10.5 4.512092 0.71342439 Florida subtracted from 40 10,025 5.2598503 0.83165536 Difference Lower UpperP-value 1.6 -1.6585489 4.8585489 0.3145 0,475 -2.7835489 3,7335489 0.9019 40 11.625 4.9130256 0.77681755 New York North Carolina New York subtracted from ANOVA table Source DF Location 254,016667 27,008333 1.1228081 0.3288 Error 117 2814.35 24.054274 Total 119 2868.3667 MS F-Stat P-value Difference Lower UpperP-value North Carolina -1.1254.3835489 2.1335489 0.5621

Explanation / Answer

Sol:

Anova one way

H0:all three group means are equal

H1:atleast one of the group means are different.

Ho:?1=?2=?3
Ha: some differences in the means

? = 0.01

F=1.123

probability=p=0.329

p>alpha

Fail to reject Ho

Interpret: At the 0.01 level, there is not significant evidence to conclude there is some difference in the mean depression score/geographic location for adults 65 and older across the three geographic locations.

since it is not significant not appropriate to consider multiple comparisons

Which of the multiple comparisons are significant?

(d) It is not appropriate to consider multiple comparisons

ANSWERS IN BOLD

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