Question

Question 1. The following table summarizes the results of the test.

	2014	2015
Mean	57.50	70.00
Variance	173.61	172.22
Observations	10	10
P Value	0.048
t Critical two-tail	2.101

Here p value= 0.04

a) Use the information in the table to justify whether there is a significant difference between the sales of two years.

b) Have Fatima's promotional techniques been more effective than the ones used last year? Explain.

Question 2. Fatima also wants to reward the sales manager of the branch that has performed the best during the New Year week. She has selected the top three branches with the highest sales, and will conduct Analysis of Variance (ANOVA) on the data set.

What will an ANOVA help her decide?

Branch Sales (AED '000)
Branch 1	43	39	55	56	73
Branch 2	55	58	66	79	82
Branch 3	61	66	85	86	91

Answer 1

1.

(a)

We reject our null hypothesis if , level of significance.

We generally test for level of significance 0.10, 0.05 or something like these.

So, we reject our null hypothesis which corresponds to indifference in sales in two years.

(b)

We observe that mean sale increased. Hence, based on the given data we can conclude that there is significant evidence that Fatima's promotional techniques have been more effective than the ones used last year.

2.

We have to compare among more than two (three here) groups. So, we have to perform analysis of variance i.e. ANOVA.

We have to test for null hypothesis

against the alternative hypothesis

Our test statistic is given by

Here,

Number of groups

Number of observations in different groups are

Total number of observations

Mean of different groups are as follows

Grand mean is given by

Between groups mean sum of squares is given by

Within groups mean sum of squares is given by

Degrees of freedom

[Using R-code '1-pf(4.570123,2,12)']

We reject our null hypothesis if , level of significance.

We generally test for level of significance 0.10, 0.05 or something like these.

So, we reject our null hypothesis.

Thus based on the given data we can conclude that there is significant evidence that means are not equal for different branches.

Hence, Fatima will decide that mean sales are significantly different for different branches.