Question

QUESTION 5 The pumber of grams of fat per serving for three different kinds of burger from several marylfacturers is listed below. Beef Burger Chicken Burger Fish Burger 23 25 26 24 26 26 41 26 43 24 24 36 27 25 39 28 25 23 32 i) At the 0.05 level of significance, is there sufficient evidence to conclude a difference in the mean of fat content? (16 marks) i) Construct the ANOVA Summary Table from the derived statistics. 4 marks)

Answer 1

(i)

H0: Null Hypothesis:

HA: Alternative Hypothesis: (At least one population mean is different from the other two population means)

From the given data, the following statistics are calculated:

DATA SUMMARY

Burger	n	Mean ()	Std. Dev. (s)
Beef Burger	8	29.625	7.6893
Chicken Burger	7	29	7.9582
Fish Burger	6	28.5	6.091

Overall mean = = (29.625 + 29 + 28.5)/3 = 29.0417

k = Number of Groups = 3

Between Group Degrees of Freedom = k -1

= 3 - 1 = 2

N = Total number of subjects = 8 + 7 + 6 = 21

Within Group Degrees of Freedom = N - k = 21 - 3 = 18

Total Degrees of Freedom = N - 1 = 21 - 1 = 20

Sum of Squares Between Groups (SS_B) is given by:

3 SSB = Σ ni(zi-r)2 = 4.4345

Sum of Squares Within Groups (SS_W) is given by:

,

where s_i is the Standard Deviation of the i-th Group.

Total Sum of Squares (SS_T) is given by:

Mean Square Between Groups (MS_B) is given by:

$MS_{B}=rac{SS_{B}}{k-1}=rac{4.4345}{3-1}=2.2173$

Mean Square Within Groups (MS_W) is iven by:

$MS_{W}=rac{SS_{W}}{N-k}=rac{979.3764}{21-3}=54.4098$

F statistic is given by:

$F=rac{MS_{B}}{MS_{W}}=rac{2.2173}{54.4098}=0.0408$

Degrees of Freedom for Numerator = 2

Degrees of Freedom for Denominator = 18

By Technology, P- Value = 0.9602

Since P - Value = 0.9602 is greater than = 0.05, the difference is not significant. Fail to reject null hypothesis.

Conclusion:

There is not sufficient evidence to conclude a diffrence in the mean of fat content.

(ii)

ANOVA Summary Table is given below:

Source of Variation	Degrees of Freedom	Sum of Squares	Mean Square	F - Stat	P - Value
Between Groups	2	4.4345	2.2173	0.0408	0.9602
Within Groups	18	979.3764	54.4098
Total	20	983.811