Question

Estimation and Hypothesis Test (1 sample)

As an employee of a Retail Store and a recent graduate of the Accounting Program, you are responsible for an advertising campaign aimed at increasing the amount spent by customers.

After the advertising campaign, a random sample of 50 customers and the amount spent at the store was recorded as follows:

Amount spent:                          $150, 122, 210, 183, 50, 423, 158, 281, 190, 260,

                                                   180, 125, 210, 188, 224, 253, 320, 243, 180, 363,

                                                   220, 180, 240, 230, 180, 200, 460, 130, 72, 165

                                                   130, 252, 44, 134, 467, 412, 188, 352, 189, 318

                                                   120, 220, 240, 245, 80, 225, 268, 108, 220, 480

1. What is the best estimate of the average amount a buying customer spent at the store after the advertising campaign?

2. Determine the 90% confidence interval for the average amount spent at the store after the advertising campaign. Interpret its meaning.

3. Before the advertising campaign, the average amount spent at the store is $ 175.

Perform a hypothesis test to determine if there is sufficient evidence that the advertising campaign didn’t change the average amount a customer spent at the store. Test at 2% significance level. (Include null and alternative Hypothesis, test statistics, critical value, reject region, and conclusion

Answer 1

Sr.	X	X^2
1	150	22500
2	122	14884
3	210	44100
4	183	33489
5	50	2500
6	423	178929
7	158	24964
8	281	78961
9	190	36100
10	260	67600
11	320	102400
12	243	59049
13	180	32400
14	363	131769
15	180	32400
16	125	15625
17	210	44100
18	188	35344
19	224	50176
20	253	64009
21	460	211600
22	130	16900
23	72	5184
24	165	27225
25	220	48400
26	180	32400
27	240	57600
28	230	52900
29	180	32400
30	200	40000
31	188	35344
32	352	123904
33	189	35721
34	318	101124
35	130	16900
36	252	63504
37	44	1936
38	134	17956
39	467	218089
40	412	169744
41	268	71824
42	108	11664
43	220	48400
44	480	230400
45	120	14400
46	220	48400
47	240	57600
48	254	64516
49	80	6400
50	225	50625
Total	11091	2984359
Mean	221.82
SD	103.4263

Mean =

SD =

a. What is the best estimate of the average amount a buying customer spent at the store after the advertising campaign?

Mean =

Since we do not have the population SD we will use t-dist.

b. Determine the 90% confidence interval for the average amount spent at the store after the advertising campaign. Interpret its meaning.

(1- )% is the confidence interval for population mean

Where 221.82

Alpha =1 - 0.90 = 0.10

Therefore the C.V. =

=

= 1.6766 .............found using t-dist tables

Substituting the vlaue

c. Before the advertising campaign, the average amount spent at the store is $ 175.

Perform a hypothesis test to determine if there is sufficient evidence that the advertising campaign didn’t change the average amount a customer spent at the store. Test at 2% significance level. (Include null and alternative Hypothesis, test statistics, critical value, reject region, and conclusion

We peviously assume the mean to $175. We are testing if the population mean is different from these.

Test Stat =

Where the null mean = 175

Test stat =

Critical value with = 2%. This is a two tailed test therefore

=

C.V. = .............using t-dist tables

Since Test stat > C.V.

We reject the null hypothesis at 2%.

We conclude that the population mean is significantly different from $175.