Introduction
This paper reports the results of hypothesis test conducted on eleven variables captured in the Springdale community shopping survey. The null hypothesis was rejected in nine out of the eleven variables analyzed.
Analysis
- Mean and standard deviation
Springdale Mall
Mean = 3.813
Standard deviation = 1.064
Downtown
Mean = 3.407
Standard deviation = 1.124
West Mall
= 3.287
Standard deviation = 1.183
- Hypothesis testing
Springdale
Null hypothesis: H0: µ = 3.0
Alternative hypothesis: H1: µ ≠ 3.0
T-calculated = (- ∆) ÷ (/)
Where ∆ = 3.0
9.360
T-critical = 1.655
T-calculated value is greater than upper t-critical value
Null hypothesis is rejected
Downtown
Null hypothesis: H0: µ = 3.0
Alternative hypothesis: H1: µ ≠ 3.0
T-calculated = (- ∆) ÷ (/)
Where ∆ = 3.0
4.432
T-critical = 1.655
T-calculated value is greater than upper t-critical value
Null hypothesis is rejected
/>
West Mall
Null hypothesis: H0: µ = 3.0
Alternative hypothesis: H1: µ ≠ 3.0
T-calculated = (- ∆) ÷ (/)
Where ∆ = 3.0
2.967
T-critical = 1.655
T-calculated value is greater than upper t-critical value
Null hypothesis is rejected
- Confidence interval
Springdale Mall
= 3.813
Standard deviation = 1.064
The z-score for 90% confidence level is 1.645
Sample size n = 150
Confidence interval = ± z.
3.813 ± [1.645 X (1.064 ÷ 12.247)
3.670 < < 3.956
The neutral value (3.0) does not fall within the confidence interval. Consequently, the null hypothesis is rejected.
Downtown
= 3.407
Standard deviation = 1.124
Confidence interval = ± z.
3.407± [1.645 X (1.124 ÷ 12.247)
3.256 < < 3.558
The neutral value (3.0) does not fall within the confidence interval. Consequently, the null hypothesis is rejected.
West Mall
= 3.287
Standard deviation = 1.183
Confidence interval = ± z.
- ± [1.645 X (1.183 ÷ 12.247)
3.128 < < 3.446
The neutral value (3.0) does not fall within the confidence interval. Consequently, the null hypothesis is rejected.
- P-values
Springdale
1.16 X 10-16
Downtown
1.80 X 10-5
West mall
3.51 X 10-4
- Hypothesis testing
Easy to return/exchange goods
Null hypothesis: H0: k = 0.3
Alternative hypothesis: H1: k ≠ 0.3
Z-calculated = (p - Ṕ) ÷ [Ṕ (1- Ṕ) ÷ n]
Where Ṕ = and p =
3.127
Z-critical = 1.96
Z-calculated value is greater than upper z-critical value
Null hypothesis is rejected
High quality of goods
Null hypothesis: H0: k = 0.3
Alternative hypothesis: H1: k ≠ 0.3
Z-statistic = (p - Ṕ) ÷ [Ṕ (1- Ṕ) ÷ n]
Where Ṕ = and p =
5.033
Z-critical = 1.96
Z-calculated value is greater than upper z-critical value
Null hypothesis is rejected
Low prices
Null hypothesis: H0: k = 0.3
Alternative hypothesis: H1: k ≠ 0.3
Z-statistic = (p - Ṕ) ÷ [Ṕ (1- Ṕ) ÷ n]
Where Ṕ = and p =
-3.802
Z-critical = 1.96
Z-calculated value is less than lower z-critical value
Null hypothesis is rejected
Good variety of sizes/styles
Null hypothesis: H0: k = 0.3
Alternative hypothesis: H1: k ≠ 0.3
Z-statistic = (p - Ṕ) ÷ [Ṕ (1- Ṕ) ÷ n]
Where Ṕ = and p =
8.498
Z-critical = 1.96
Z-calculated value is greater than upper z-critical value
Null hypothesis is rejected
Sales staff helpful/friendly
Null hypothesis: H0: k = 0.3
Alternative hypothesis: H1: k ≠ 0.3
Z-statistic = (p - Ṕ) ÷ [Ṕ (1- Ṕ) ÷ n]
Where Ṕ = and p =
1.914
Z-critical = 1.96
Z-calculated value is greater than lower z-critical value but less than upper z-critical value
Null hypothesis is upheld
Convenient shopping hours
Null hypothesis: H0: k = 0.3
Alternative hypothesis: H1: k ≠ 0.3
Z-statistic = (p - Ṕ) ÷ [Ṕ (1- Ṕ) ÷ n]
Where Ṕ = and p =
6.072
Z-critical = 1.96
Z-calculated value is greater than upper z-critical value
Null hypothesis is rejected
Clean stores and surroundings
Null hypothesis: H0: k = 0.3
Alternative hypothesis: H1: k ≠ 0.3
Z-statistic = (p - Ṕ) ÷ [Ṕ (1- Ṕ) ÷ n]
Where Ṕ = and p =
8.151
Z-critical = 1.96
Z-calculated value is greater than upper z-critical value
Null hypothesis is rejected
A lot of bargain sales
Null hypothesis: H0: k = 0.3
Alternative hypothesis: H1: k ≠ 0.3
Z-statistic = (p - Ṕ) ÷ [Ṕ (1- Ṕ) ÷ n]
Where Ṕ = and p =
-0.05
Z-critical is 1.96
Z-calculated value is greater than lower z-critical value but less than upper z-critical value
Null hypothesis is upheld
- P-values
Easy to return/exchange goods
1.77 X 10-3
High quality of goods
4.83 X 10-7
Low prices
1.43 X 10-4
Good variety of sizes/styles
0.00
Sales staff helpful/friendly
5.56 X 10-2
Convenient shopping hours
1.26 X 10-9
Clean stores and surroundings
4.44 X 10-14
A lot of bargain sales
- X 10-1
- Strengths and weakness
More than one third of the respondents selected Springdale as the best shopping area in seven out of eight variables. Springdale principal strengths were high quality high quality of goods, good variety of sizes, convenient shopping hours and clean stores and surroundings. Its principal weaknesses were unfriendly staff and low bargain sales.
Conclusion
Null hypotheses for nine out of eleven variables were rejected. Meaning, that there were significant difference between the neutral values or proportion and the sample mean or observed proportion for most variables.
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