Question

(3) Malls face increasing completion from Amazon. Last year the average consumer spent $50 at the local mall. Is consumer spending decreasing? This year, in a random sample of shoppers, each was asked how much money she/he spent on the last trip to the local mall. Do they data support at a=10% significance level the research hypothesis that average shopper this year spent less that $50?

   a. What are the null and alternative hypotheses?

   b. What is the appropriate p-value?

   c. Can they infer at the 10% significance level that consumer spending decreased since last year? State your conclusion.

Consumer Spending
$       54.88
$       32.81
$       42.84
$       34.75
$       64.45
$       43.76
$       46.56
$       39.45
$       54.25
$       50.78
$       33.86
$       44.31
$       56.61
$       35.02
$       29.42
$       53.53
$       82.91
$       33.40
$       54.90
$       43.07
$       57.16
$       55.89
$       37.21
$       40.60
$       47.09
$       57.19
$       30.19
$       64.56
$       54.18
$       61.05
$       44.26
$       55.59
$       69.89
$       50.18
$       52.08
$       44.97
$       60.56
$       41.90
$       61.05
$       55.94
$       51.43
$       43.11
$       61.13
$       37.41
$       48.33
$       41.46
$       37.78
$       54.32
$       45.62
$       61.68
$       52.47
$       42.88
$       43.15
$       55.39
$       43.01
$       47.93
$       48.12
$       47.68
$       61.72
$       49.53
$       61.75
$       45.04
$       41.59
$       57.66
$       31.66
$       47.72
$       33.90
$       50.32
$       43.22
$       48.07
$       48.42
$       52.58
$       59.25
$       36.57
$       70.23
$       48.08
$       60.11
$       58.14
$       60.73
$       65.73
$       53.19
$       48.95
$       61.29
$       19.56
$       59.92
$       41.50
$       48.36
$       44.44
$       46.34
$       49.35
$       43.52
$       51.96
$       54.89
$       30.68
$       54.74
$       36.38
$       45.55
$       38.03
$       46.97
$       39.56
$       42.98
$       56.00
$       46.23
$       50.77
$       46.89
$       43.97
$       28.55
$       32.10
$       38.54
$       41.21
$       52.71
$       28.89
$       24.70
$       53.83
$       54.92

Answer 1

	Values ( X )
	54.88	46.6803
	32.81	232.1875
	42.84	27.1201
	34.75	176.8288
	64.45	269.0354
	43.76	18.3844
	46.56	2.2133
	39.45	73.9204
	54.25	38.4685
	50.78	7.4655
	33.86	201.2908
	44.31	13.9704
	56.61	73.313
	35.02	169.721
	29.42	346.9912
	53.53	30.0556
	82.91	1215.38
	33.4	214.5551
	54.9	46.954
	43.07	24.7775
	57.16	83.034
	55.89	61.5017
	37.21	117.4557
	40.6	55.4682
	47.09	0.9172
	57.19	83.5816
	30.19	318.8974
	64.56	272.6561
	54.18	37.6051
	61.05	169.0598
	44.26	14.3467
	55.59	56.8863
	69.89	477.0861
	50.18	4.5467
	52.08	16.2594
	44.97	9.4722
	60.56	156.5577
	41.9	37.7942
	61.05	169.0598
	55.94	62.2884
	51.43	11.44
	43.11	24.3809
	61.13	171.1466
	37.41	113.1607
	48.33	0.0797
	41.46	43.3978
	37.78	105.4257
	54.32	39.3417
	45.62	5.8937
	61.68	185.8396
	52.47	19.5567
	42.88	26.7051
	43.15	23.9875
	55.39	53.9094
	43.01	25.3784
	47.93	0.0139
	48.12	0.0052
	47.68	0.1352
	61.72	186.9318
	49.53	2.1972
	61.75	187.753
	45.04	9.0463
	41.59	41.7019
	57.66	92.3963
	31.66	268.5567
	47.72	0.1074
	33.9	200.1574
	50.32	5.1633
	43.22	23.3067
	48.07	0.0005
	48.42	0.1386
	52.58	20.5417
	59.25	125.4915
	36.57	131.7376
	70.23	492.0544
	48.08	0.001
	60.11	145.4991
	58.14	101.8545
	60.73	160.8407
	65.73	312.6637
	53.19	26.4432
	48.95	0.8141
	61.29	175.3585
	19.56	811.5491
	59.92	140.9515
	41.5	42.8724
	48.36	0.0975
	44.44	13.0155
	46.34	2.9162
	49.35	1.696
	43.52	20.5001
	51.96	15.3061
	54.89	46.8171
	30.68	301.637
	54.74	44.7869
	36.38	136.1352
	45.55	6.2385
	38.03	100.3543
	46.97	1.1614
	39.56	72.0411
	42.98	25.6816
	56	63.2391
	46.23	3.304
	50.77	7.4109
	46.89	1.3403
	43.97	16.6276
	28.55	380.1603
	32.1	254.3291
	38.54	90.3964
	41.21	46.7541
	52.71	21.737
	28.89	367.0175
	24.7	545.1151
	53.83	33.435
	54.92	47.2285
Total	5525.49	12656.1944

To Test :-

H₀ :-

H₁ :-  

Test Statistic :-

Test Criteria :-  

P value

Looking for the | t | = 1.987 across n - 1 = 115 - 1 degree of freedom

| t | lies between the values 1.984 and 2.364 repsective P value are 0.025 and 0.01.

Using excel to calculate the exact P value = 0.02466

Decision based on P value

Reject null hypothesis if P value < level of significance

0.02466 < 0.10, we reject null hypothesis

Part c)

Conclusion :- Accept Alternative Hypothesis

There is sufficient evidence to suppir tthe claim that average shopper this year spent less that $50.