This dataset shows you the startup costs for various stores. One of your best fr
ID: 2927021 • Letter: T
Question
This dataset shows you the startup costs for various stores. One of your best friends, Paul states that the average startup costs for any type of businesses are the same. As a student, you want to conduct a test to check if her statement is correct or not. Please write a null hypothesis and alternative hypothesis. Then, use SPSS for one-way ANOVA test. Please briefly interpret the testing result.
# Store Cost($1K) 1 pizza 80 2 pizza 125 3 pizza 35 4 pizza 58 5 pizza 110 6 pizza 140 7 pizza 97 8 pizza 50 9 pizza 65 10 pizza 79 11 pizza 35 12 pizza 85 13 pizza 120 14 baker/donuts 150 15 baker/donuts 40 16 baker/donuts 120 17 baker/donuts 75 18 baker/donuts 160 19 baker/donuts 60 20 baker/donuts 45 21 baker/donuts 100 22 baker/donuts 86 23 baker/donuts 87 24 baker/donuts 90 25 shoe store 48 26 shoe store 35 27 shoe store 95 28 shoe store 45 29 shoe store 75 30 shoe store 115 31 shoe store 42 32 shoe store 78 33 shoe store 65 34 shoe store 125 35 gift shops 100 36 gift shops 96 37 gift shops 35 38 gift shops 99 39 gift shops 75 40 gift shops 150 41 gift shops 45 42 gift shops 100 43 gift shops 120 44 gift shops 50 45 pet store 25 46 pet store 80 47 pet store 30 48 pet store 35 49 pet store 30 50 pet store 28 51 pet store 20 52 pet store 75 53 pet store 48 54 pet store 20 55 pet store 50 56 pet store 75 57 pet store 55 58 pet store 60 59 pet store 85 60 pet store 110Explanation / Answer
The null hypothesis is mean values of start up cost among pizza, baker/donuts, shoe store, gift shops and pet store are same for all groups.
Alternative hypothesis is mean values of startare cost among pizza, baker/donuts, shoe store, gift shops and pet store is not same for all groups. cost among pizza, baker/donuts, shoe store, gift shops and pet store is not same for all groups.
After doing One ANOVA analysis in SPSS output shows P value for between the group difference is .018 suggest that there is statistically significantly different in mean startup cost in at least two groups
With ANOVA,we observed that the null hypothesis is rejected, then we can interpretate that at least 2 groups are different from each other. In order to determine which groups are different from which, post-hoc t-tests are performed using some form of correction (such as the Bonferroni correction) to adjust for an inflated probability of a Type I error.
Post doc test suggests that baker/donuts vs pet store had mean difference of 40.46 and P value = 0.029. This finding tell us that there is significant difference in average startup costs between baker/donut and pet store.
ANOVA output of SPSS output is given below
Descriptives
cost
N
Mean
Std. Deviation
Std. Error
95% Confidence Interval for Mean
Minimum
Maximum
Between- Component Variance
Lower Bound
Upper Bound
Pizza
13
83.00
34.135
9.467
62.37
103.63
35
140
baker/donuts
11
92.09
38.893
11.727
65.96
118.22
40
160
shoe store
10
72.30
31.365
9.919
49.86
94.74
35
125
gift shops
10
87.00
35.904
11.354
61.32
112.68
35
150
pet store
16
51.63
27.075
6.769
37.20
66.05
20
110
Total
60
75.18
35.620
4.599
65.98
84.38
20
160
Model
Fixed Effects
33.183
4.284
66.60
83.77
Random Effects
7.839
53.42
96.95
207.999
Test of Homogeneity of Variances
cost
Levene Statistic
df1
df2
Sig.
.325
4
55
.860
ANOVA
cost
Sum of Squares
df
Mean Square
F
Sig.
Between Groups
14298.224
4
3574.556
3.246
.018
Within Groups
60560.759
55
1101.105
Total
74858.983
59
Multiple Comparisons
cost
Bonferroni
(I) store_type
(J) store_type
Mean Difference (I-J)
Std. Error
Sig.
95% Confidence Interval
Lower Bound
Upper Bound
Pizza
baker/donuts
-9.091
13.594
1.000
-48.85
30.67
shoe store
10.700
13.957
1.000
-30.12
51.52
gift shops
-4.000
13.957
1.000
-44.82
36.82
pet store
31.375
12.390
.142
-4.86
67.61
baker/donuts
Pizza
9.091
13.594
1.000
-30.67
48.85
shoe store
19.791
14.499
1.000
-22.61
62.20
gift shops
5.091
14.499
1.000
-37.31
47.50
pet store
40.466*
12.997
.029
2.45
78.48
shoe store
Pizza
-10.700
13.957
1.000
-51.52
30.12
baker/donuts
-19.791
14.499
1.000
-62.20
22.61
gift shops
-14.700
14.840
1.000
-58.10
28.70
pet store
20.675
13.376
1.000
-18.45
59.80
gift shops
Pizza
4.000
13.957
1.000
-36.82
44.82
baker/donuts
-5.091
14.499
1.000
-47.50
37.31
shoe store
14.700
14.840
1.000
-28.70
58.10
pet store
35.375
13.376
.106
-3.75
74.50
pet store
Pizza
-31.375
12.390
.142
-67.61
4.86
baker/donuts
-40.466*
12.997
.029
-78.48
-2.45
shoe store
-20.675
13.376
1.000
-59.80
18.45
gift shops
-35.375
13.376
.106
-74.50
3.75
*. The mean difference is significant at the 0.05 level.
Descriptives
cost
N
Mean
Std. Deviation
Std. Error
95% Confidence Interval for Mean
Minimum
Maximum
Between- Component Variance
Lower Bound
Upper Bound
Pizza
13
83.00
34.135
9.467
62.37
103.63
35
140
baker/donuts
11
92.09
38.893
11.727
65.96
118.22
40
160
shoe store
10
72.30
31.365
9.919
49.86
94.74
35
125
gift shops
10
87.00
35.904
11.354
61.32
112.68
35
150
pet store
16
51.63
27.075
6.769
37.20
66.05
20
110
Total
60
75.18
35.620
4.599
65.98
84.38
20
160
Model
Fixed Effects
33.183
4.284
66.60
83.77
Random Effects
7.839
53.42
96.95
207.999
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