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:μ1=μ2=μ3Ho:μ1=μ2=μ3
    Ha:μ1≠μ2≠μ3Ha:μ1≠μ2≠μ3
  • Ho:μ1=μ2=μ3Ho:μ1=μ2=μ3
    Ha:Ha: some differences in the means
  • Ho:μ1≠μ2≠μ3Ho:μ1≠μ2≠μ3
    Ha:μ1=μ2=μ3Ha:μ1=μ2=μ3
• αα = ___
• TS: f = ___ (round your answer to 3 decimal places)
• probability = _____
• Decision: ___ (reject H₀ fail to reject H₀)
• 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."
• Which of the multiple comparisons are significant?
  • FL vs. NY
  • FL vs. NC
  • NY vs. NC
  • It is not appropriate to consider multiple comparisons

Transcribed Image Text:

Response statistics by factor Tukey 99% Simultaneous Confidence Intervals: Location + n+ Mean + Std. Dev. + Std. Error + Florida subtracted from Florida 40 10.025 5.2598503 0.83165536 Difference Lower Upper P-value New York 40 11.625 4.9130256 0.77681755 New York 1.6 -1.6585489 4.8585489 0.3145 North Carolina 40 10.5 4.512092 0.71342439 North Carolina 0.475 -2.7835489 3.7335489 0.9019 ANOVA table New York subtracted from Source DF SS MS F-Stat p-value Difference Lower Upper P-value Location 2 54.016667 27.008333 1.1228081 0.3288 North Carolina -1.125 -4.3835489 2.1335489 0.5621 Error 117 2814.35 24.054274 Total 119 2868.3667 Response statistics by factor Tukey 99% Simultaneous Confidence Intervals: Location + n+ Mean + Std. Dev. + Std. Error + Florida subtracted from Florida 40 10.025 5.2598503 0.83165536 Difference Lower Upper P-value New York 40 11.625 4.9130256 0.77681755 New York 1.6 -1.6585489 4.8585489 0.3145 North Carolina 40 10.5 4.512092 0.71342439 North Carolina 0.475 -2.7835489 3.7335489 0.9019 ANOVA table New York subtracted from Source DF SS MS F-Stat p-value Difference Lower Upper P-value Location 2 54.016667 27.008333 1.1228081 0.3288 North Carolina -1.125 -4.3835489 2.1335489 0.5621 Error 117 2814.35 24.054274 Total 119 2868.3667

Answer rating: 100% (QA)

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