Question

You want to determine whether there is a statistically different average weekly sales between Sales Rep A and Sales Rep B.

* Create Null and Alternative Hypothesis statements that would allow you to determine whether their sales performance is statistically different or not.

* Use a significance level of .05 to conduct a t-test of independent samples to compare the average weekly sales of the two candidates.

* Calculate the p-value?

SAMPLE OF WEEKLY SALES
Sales Rep #	AverageWeekly Sales($)		Week #	Weekly Sales($) - Rep A	Weekly Sales($) - Rep B
1	1228		1	4657	5839
2	7374		2	6133	2602
3	1055		3	3438	2830
4	1859		4	7394	4763
5	3938		5	4327	3740
6	1692		6	2552	2315
7	569		7	7063	1599
8	4059		8	7844	1629
9	3689		9	6898	2416
10	607		10	4003	2107
11	1370		11	6884	4237
12	3735		12	4007	6322
13	3305		13	7214	3710
14	7228		14	2358	5890
15	6279		15	7745	5119
16	1671		16	1337	5184
17	5708		17	1052	3439
18	2569		18	6056	4828
19	4163		19	1495	3667
20	1519		20	3530	3518
21	7734		21	4749	6073
22	784		22	3833	5566
23	6766		23	7869	4555
24	7261		24	4541	5867
25	5034		25	6882	6039
26	7115		26	3868	1032
27	6291		27	5934	4834
28	6287		28	4447	3687
29	2080		29	5504	5500
30	7621		30	5554	4659
31	1047
32	6517
33	5172
34	3876
35	5429
36	4538
37	3786
38	2510
39	4863
40	7246
41	1175
42	641
43	4269
44	7034
45	3406
46	2256
47	3182
48	5178
49	4428
50	1189

Answer 1

Null hypothesis H0 : =     

Alternative hypothesis Ha :

is the mean weekly sales rep A and   is the mean weekly sales rep B.

First we have to perform F test to check the significance between the variances of two weekly sales data sets,

Using the excel function =FTEST( data set1, data set 2)

Using this function we got the p value = 0.1375 , we are given = 0.05

As p value is greater than , variances of the two data sets are not significantly different .( they are equal ) Therefore we have to used pooled variance 2 sample t test.

( Since Ha consist of sign , this test become two tailed test )

I have used excel to perform pooled variance ( or equal variance ) 2 sample t test for the given data set.

Go to Data menu ---> Data analysis ---> t-Test: Two-Sample Assuming Equal Variances and click on OK.

Then Input for variable 1 : Select the all numbers in column Rep A

For variable 2 : select the all numbers in column Rep B

Set hypothesis mean difference = 0 and check the box for Labels then click on OK.

The following output will be appeared :

So according to the results t test statistic = 1.85 ( rounded to 2 decimal places )

p value of the t test = 0.0695

Decision rule :  if p value is less than then, reject the null H0

  if p value is greater than then, fail to reject the null H0 .

We are given = 0.05

As p value (0.0695 ) is greater than (0.05) we fail to reject the null H0

Conclusion : There is no significant difference between mean weekly sales rep A and   is the mean weekly sales rep B.