Answer to Question #203762 in Statistics and Probability for ejaz

Question

1. Pepsi Co. Pvt Ltd is planning to produce a new energy drink. For this purpose, a pilot study was conducted using four different energy drinks formula. They were tested on 3 different sets of people and the reactions in energy level of the people were measured forming four groups. Using the data (measured energy level values) provided below, test whether there is difference in the four energy drinks. Perform this by finding F ratio. What is critical F value, i.e. Fc at 95% confidence interval?. The data is as shown in Table 1.

 

Formula 1

Formula 2

Formula 3

Formula 4

64

46

43

38

55

42

32

45

80

42

45

37

Answer 1

Variance:

$s=\frac{\sum(x_i-\mu)^2}{n-1}$

Variances of four groups:

$s_1=10.33$

$s_2=25.33$

$s_3=122.33$

$s_4=52.33$

F-statistics:

$F_1=\frac{s^2_1}{s^2_2}=0.1663$

$F_2=\frac{s^2_1}{s^2_3}=0.0071$

$F_3=\frac{s^2_1}{s^2_4}=0.0390$

$F_4=\frac{s^2_2}{s^2_3}=0.0429$

$F_5=\frac{s^2_2}{s^2_4}=0.2343$

$F_6=\frac{s^2_3}{s^2_4}=5.4647$

$df_1=a-1=4-1=3$

$df_2=N-a=12-4=8$

where a is the number of groups,

N is the total number of subjects in the experiment.

Critical value:

$F_{3,8}=2.92380$

Since only $F_6>F_{3,8}$ , we can conclude that there is difference between Formula1 and Formula4 only.