Question

1. Using the Data Set, create and calculate the following in Excel^®:

Determine the range of values in which you would expect to find the average weekly sales for the entire sales force in your company 90% of the time, and calculate the following:

A. The impact of increasing the confidence level to 95%

B. The impact of increasing the sample size to 150, assuming the same mean and standard deviation, but allowing the confidence level to remain at 90%

Data Set:

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

Answer:

Determine the range of values in which you would expect to find the average weekly sales for the entire sales force in your company 90% of the time

We want to calculate the 90% confidence interval of average weekly sales.

The significance level

We want to find the critical value , that is

From ,the standard normal tables we get

the average of the average weekly sales of n=50 reps is given by

The sample standard deviation s, is given by

Using, the sample standard deviation as an estimate of the population standard deviation, the standard error of mean is

The lower confidence interval is

the upper level of confidence interval is

Part (A)

Impact of increasing the confidence level to 95%

The significance level . the critical value is the value of Z for which

Using standard normal tables we get

The lower confidence interval is

the upper level of confidence interval is

The increase in the confidence interval from 90% to 95% has given us a larger interval.

Part(B)

Calculate the impact of increasing the sample size to 150, assuming the same mean and standard deviation, but allowing the confidence level to remain at 90%?

Confidence Interval Estimate for the Mean
Data
Sample Standard Deviation	2284.1933
Sample Mean	3966.64
Sample Size	150
Confidence Level	90%
Intermediate Calculations
Standard Error of the Mean	186.503602
Degrees of Freedom	149
t Value	1.6551
Interval Half Width	308.6904
Confidence Interval
Interval Lower Limit	3657.9496
Interval Upper Limit	4275.3304

90% CI = (3657.9496, 4275.3304)

By increasing ,the sample size to 150, assuming the same mean and standard deviation, but allowing the confidence level to remain at 90%, the width of the interval is decreased.