29. Remember those Public Works and Public Safety employees from Quiz 4? The Pub
ID: 3438244 • Letter: 2
Question
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
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
Explanation / Answer
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.
---------------------------------------
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.
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 196 6272.563 Source of Variation SS df MS F P-value F crit Between Groups 305.29 2 152.645 4.2284237 0.0159 2.30259 Within Groups 6967.25 193 36.0997409 Total 7272.54 195Related Questions
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