Question

A bank wants to know if the enrollment for new savings accounts has improved at various branches after offering a free iPhone X to customers. Use the data from "iphoneX" sheet in excel

Run the appropriate statistical test with α=0.05. Which of the following are correct? More than one answer is possible.

		There was a decrease of 0.7 people enrolled on average in a new savings account after offering a free iPhone X.
		There was an increase of 0.7 people enrolled on average in a new savings account after offering a free iPhone X.
		The test was NOT statistically significant at α=0.05
		The test was statistically significant at α=0.05

before iPhoneX	after iPhoneX
69	34
35	28
28	11
9	45
50	88
24	89
31	25
6	2
88	54
19	20
31	95
74	94
7	74
21	1
17	28
82	100
24	71
84	42
88	29
72	2
13	24
55	70
22	11
25	34
38	2
15	14
3	56
83	52
59	80
96	14

Answer 1

before iPhoneX	after iPhoneX	Difference
69	34	35
35	28	7
28	11	17
9	45	-36
50	88	-38
24	89	-65
31	25	6
6	2	4
88	54	34
19	20	-1
31	95	-64
74	94	-20
7	74	-67
21	1	20
17	28	-11
82	100	-18
24	71	-47
84	42	42
88	29	59
72	2	70
13	24	-11
55	70	-15
22	11	11
25	34	-9
38	2	36
15	14	1
3	56	-53
83	52	31
59	80	-21
96	14	82

Sample mean of the difference using excel function AVERAGE(), x̅_d = -0.7000

Sample standard deviation of the difference using excel function STDEV.S(), s_d = 39.2544

Sample size, n = 30

Null and Alternative hypothesis:

Ho : µ_d = 0    

H1 : µ_d ≠ 0    

Test statistic:     

t = (x̅_d)/(s_d/√n) = -0.0977    

df = n-1 = 29    

Critical value :     

Two tailed critical value, t_c = T.INV.2T(0.05,29) = 2.0452

p-value :     

Two tailed p-value = T.DIST.2T(-0.0977,29) = 0.9229

Decision:     

p-value > α, Do not reject the null hypothesis.

Answer: There was a decrease of 0.7 people enrolled on average in a new savings account after offering a free iPhone X.

The test was NOT statistically significant at α=0.05