29 Remember those Public Works and Public Safety employees f

29. Remember those Public Works and Public Safety employees from Quiz 4? The Public Works, Public Safety, and Fire Department are the largest of the municipal population in a city. The city, continuing to be concerned about their health insurance costs, wants to see if putting money toward a weight-loss program for one or more of these groups would be beneficial.

Body Mass Index (BMI) is a common index used to measure your risk for disease that can occur with more body fat. A sample of individuals was taken from each of the above populations and each person\'s BMI was calculated. The researchers first wanted to know if there was even a difference in the average BMI between the three groups.

b. As might be expected, there was some friendly wagering between the Public Safety and the Fire groups about their BMI levels. Someone blurts out that there isn\'t any difference between the Public Safety and Fire\'s average BMI levels, so they could quit bickering.  Using the information in this problem, is there a difference in the average BMI between the Public Safety and Fire groups? You may use a 99% confidence interval if needed.  Explain clearly.

Anova: Single Factor

SUMMARY

Groups

Count

Sum

Average

Variance

Fire

52

1556.629

29.935

11.448

PS

80

2610.187

32.627

40.329

PW

64

2105.747

32.902

50.752

ANOVA

Source of Variation

SS

df

MS

F

P-value

F crit

Between Groups

0.0159

Within Groups

6967.250

Total

7272.540

Solution

First complete the ANOVA table from the information given as follows

H0: All means are equal

Ha: atleast two means are not equal

Alpha = 0.01

As p value =0.0159 > 0.01, accept null hypothesis that all means are equal at 1% sign. level.

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Comparison between public safety and fire groups:

  t = 0.3226
  df = 130
  standard error of difference = 8.345

The two-tailed P value equals 0.7475
  By conventional criteria, this difference is considered to be not statistically significant.

There is statistical evidence that two means are not different.