HYPOTHSIS TEST
- Select one variable from your project data for which the test of a proportion makes sense. If you are unsure of the variable you have chosen consult with your lecturer.
Variable Selected: Petrol Prices
- Research Question Asked:
Is there a significant difference between the unleaded petrol prices at different suburb locations?
- Statistical Hypothesis
Hypothesis Statement:
H0: There is no significant difference between the unleaded petrol prices at different suburb locations.
HA: There is a significant difference between the unleaded petrol prices at different suburb locations
Level of significance:
The α error has been chosen to be 5% – probability of committing Type1 error.
Hence the level of significance = 95% for accepting or rejecting the Null Hypothesis.
- Theoretical Test Statistics
First we check the unleaded petrol prices for normal distribution at the 7 suburb locations using the Shapiro-Wilk test:
| Tests of Normality | ||||
| Suburbloc | Shapiro-Wilk | |||
| Statistic | Df | Pvalue | ||
| Unleaded Petrol price | 1 | .919 | 66 | .000 |
| 2 | .680 | 10 | .001 | |
| 3 | .909 | 47 | .001 | |
| 4 | .830 | 48 | .000 | |
| 5 | .935 | 45 | .014 | |
| 6 | .905 | 49 | .001 | |
| 7 | .902 | 99 | .000 | |
The P value for all the 7 suburb locations are less than 0.05 and hence the unleaded petrol prices are non-normally distributed.Since we have to compare unleaded petrol prices at 7 suburb locations for non-normally distributed unleaded petrol prices we will use the Kruskal-Wallis for testing the hypothesis.
The Kruskal-Wallis gives the mean unleaded petrol prices at 7 suburb locations:
| Ranks | |||
| Suburbloc | N | Mean Rank | |
| Unleaded Petrol price | 1.00 | 66 | 154.53 |
| 2.00 | 10 | 158.70 | |
| 3.00 | 47 | 200.48 | |
| 4.00 | 48 | 180.84 | |
| 5.00 | 45 | 202.74 | |
| 6.00 | 49 | 178.47 | |
| 7.00 | 99 | 188.61 | |
| Total | 364 | ||
The Test statistic of Kruskal-Wallis gives the P value:
| Test Statisticsa,b | |
| Unleaded Petrol price | |
| Chi-Square | 8.639 |
| Df | 6 |
| Asymp. Sig. | .195 |
| a. Kruskal Wallis Test | |
| b. Grouping Variable: Suburbloc | |
Here P value = 0.195 which is greater than 0.05.
Hence at 95% level of significance, we accept the null hypothesis, that is there is no significant difference between the unleaded petrol prices at the 7 suburb locations.
Normal approximation of data:
We can take the mean of the unleaded petrol price for both the AM and PM for a given day at the 7 suburb location.
The normality test of the mean of unleaded petrol prices will yield:
| Tests of Normality | ||||
| sloc | Shapiro-Wilk | |||
| Statistic | Df | P value | ||
| UnleadedPetro | 1 | .870 | 7 | .184 |
| 2 | .681 | 4 | .007 | |
| 3 | .959 | 7 | .809 | |
| 4 | .862 | 6 | .196 | |
| 5 | .836 | 7 | .091 | |
| 6 | .911 | 6 | .440 | |
| 7 | .878 | 7 | .220 | |
As can be seen here, except for suburb location 2, rest all suburb locations have the mean unleaded petrol prices normally distributed, demonstrated by the P value > 0.05.
This demonstrates the utility of the Central Limit Theorem.
To check if the normally distributed mean of unleaded petrol prices per day show a statistically significant difference at 7 suburb location we conducted a One Way Anova:
| Test of Homogeneity of Variances | |||||||||
| UnleadedPetro | |||||||||
| Levene Statistic | df1 | df2 | P Value | ||||||
| 1.414 | 6 | 37 | .235 | ||||||
| ANOVA | |||||||||
| UnleadedPetro | |||||||||
| Sum of Squares | df | Mean Square | F | P value | |||||
| Between Groups | 151.029 | 6 | 25.171 | .650 | .690 | ||||
| Within Groups | 1432.621 | 37 | 38.719 | ||||||
| Total | 1583.649 | 43 | |||||||
The variances are similar since the test for homogeneity of variances has a P value = 0.235 which is greater than 0.05
However, there is statistically no significance found in the One way Anova test also (Pvalue = 0.690), between the mean unleaded petrol prices at 7 suburb locations.
If you want Maths management Assignment Help study samples to help you write professional custom essay’s and essay writing help.
Receive assured help from our talented and expert writers! Did you buy assignment and assignment writing services from our experts in a very affordable price.
To get more information, please contact us or visit www.myassignmenthelp.Com
