Question

Given the following companies sales of 4 brands below

Microsoft	Apple	Alibaba	Huawei
41 35 48 40 45 52	32 37 46 53 41 43	35 30 24 26 28 31	33 27 36 35 27 25

1. c) Use the analysis of variance to calculate the F-test

2. d) Make a statistic decision about the Null hypothesis

Answer 1

Here we have data:

Microsoft	Apple	Alibaba	Huawei
41	32	35	33
35	37	30	27
48	46	24	36
40	53	26	35
45	41	28	27
52	43	31	25

Here we are using Excel for calculation:

Anova: Single Factor
SUMMARY
Groups	Count	Sum	Average	Variance
Column 1	6	261	43.5	37.1
Column 2	6	252	42	52.8
Column 3	6	174	29	15.2
Column 4	6	183	30.5	22.3
ANOVA
Source of Variation	SS	df	MS	F	P-value	F crit
Between Groups	1027.5	3	342.5	10.75	0.0002	3.098
Within Groups	637	20	31.85
Total	1664.5	23

Hypothesis:

H_o : μ1 = μ2 = μ3 = μ4

H_a: At least one of the mean different from others.

Test statistics :

F = 10.75

P-value = 0.0002

Here we suppose Alpha value = 0.05

Reject the null hypothesis.

Here we have sufficient evidence to reject the null hypothesis P-value is less than Alpha value.

We can say than all the four brand mean value is not same.