Assignment 2
Part A
QUESTION 1 Table 1: Descriptive Statistics of Age | | n | Minimum | Maximum | Mean | Std. Deviation | Age (years) | 250 | 20 | 59 | 39.16 | 10.438 |

Based on Table 1, the respondents in the sample have mean age of 39.16 years with a standard deviation of 10.438 years.
The 95% confidence interval on the mean age is calculated as below:
Y±1.96σnN-nN-1
=39.16±1.9610.4382502000-2502000-1
=39.16±1.96 0.62
=39.16±1.22
=37.94 , 40.38

Conclusion:
We are 95% confident that the mean age of the population of the respondents with smoking habits is between 37.94 years and 40.38 years.

QUESTION 2 Table 2(a): Descriptive Statistics of Income for Male | | n | Minimum | Maximum | Mean | Std. Deviation | Monthly Income ($) | 120 | 1800 | 5800 | 3605.83 | 1171.962 |

Table 2(b): Descriptive Statistics of Income for Female | | n | Minimum | Maximum | Mean | Std. Deviation | Monthly Income ($) | 130 | 1800 | 5800 | 3746.15 | 1244.844 |

Table 2(a) shows that the mean and standard deviation of the income for male respondents are $3, 605.83 and $1, 171.96 respectively.
Table 2(b), on the other hand, shows that the mean and standard deviation of income for female respondents are $3, 746.15and $1, 244.84. (i) The sample mean is calculated as below:
YST= NiYiN = N1Y1+ N2Y2N = 11003605.83+9003746.152000 = 73379482000 = 3668.974

(ii) (iii) The standard error is calculated as below:
SE= 1NNi2Ni-niNi-1si2ni =1NN1 2N1-n1N1-1s12n1 + 1NN2 2N2-n2N2-1s22n2 = 12000110021100-12010991171.9622120+9002900-1308991244.8442130
= 12000110020.89211445.791+90020.85711920.281
= 1200012353671140+8274701462
= 1200020628372600
=71.813

(iv) The 95% confidence interval is calculated as below:
YST±1.96SE
=3668.974±1.9671.813
=3668.974±140.753
= 3528.22 , 3809.72

Conclusion:
We are 95% confident that the mean income for all respondents in the population is between $3, 528.22 and $3, 809.72 per month.

QUESTION 3 Table 3: Descriptive Statistics of POSITIVE | | n | Minimum | Maximum | Mean | Std. Deviation | POSITIVE | 120 | 0 | 1 | .35 | .479 |
Based on Table 3, the proportion of male respondents in the sample that had a positive response to the attitudinal question is 0.35.
The 95% confidence interval on the proportion of male customers in the population with a positive response is calculated as below: p±1.96pqnN-nN-1 =0.35±1.960.35(0.65)1201100-1201100-1
=0.35±1.960.2281209801099
= 0.35±1.960.04360.9443
=0.35±0.0807
=(0.2693 , 0.4307)

Conclusion:
We are 95% confident that the proportion of male respondents in the sample with a positive response to the attitudinal question is between 26.93% and 43.07%.

QUESTION 4
H0: The distributions of spending before being exposed to the campaign are the same for Male workers and Female workers in the population of the respondents.

H1: The distributions of spending before being exposed to the campaign are not the same for Male workers and Female workers in the population of the respondents.

Table 4(a): Ranks of Wilcoxon Rank Sum Test | | Gender | N | Mean Rank | Sum of Ranks | Before | Male | 120 | 144.28 | 17313.00 | | Female | 130 | 108.17 | 14062.00 | | Total | 250 | | |

Table 4(b): Test Statisticsa | | Before | Mann-Whitney U | 5547.000 | Wilcoxon W | 14062.000 | Z | -3.949 | Asymp. Sig. (2-tailed) | .000 | a. Grouping Variable: Gender |

The results show that: * The significance of the Wilcoxon Rank Sum Test is 0.000 which is smaller than 0.05 the level of significance for the test. Therefore, we reject the null hypothesis. * The significant value of 0.000 indicates that there is sufficient evidence from the sample to reject the null hypothesis.

Conclusion:
Based on the sample of 250 respondents, at 5% level of significance, there is sufficient evidence to conclude that the distributions of spending before being exposed to the campaign are not the same for Male workers and Female workers in the population of the respondents.

QUESTION 5
H0: The spending before the campaign exposure is the same as after, for the population of the respondents.
H1: The spending before the campaign exposure is not the same as after, for the population of the respondents.

Table 5(a): Ranks of Wilcoxon Signed Rank Test | | N | Mean Rank | Sum of Ranks | After - Before | Negative Ranks | 207a | 129.76 | 26860.00 | | Positive Ranks | 43b | 105.00 | 4515.00 | | Ties | 0c | | | | Total | 250 | | | a. After < Before | b. After > Before | c. After = Before |

Table 5(b): Test Statisticsa | | After - Before | Z | -9.762b | Asymp. Sig. (2-tailed) | .000 | a. Wilcoxon Signed Ranks Test | b. Based on positive ranks. |

The results show that: * The significant value of the Wilcoxon Signed Rank Test is 0.000, which is smaller than 0.05, the level of significance for the test. Therefore, we reject the null hypothesis. * The significant value of 0.000 indicates that there is sufficient evidence to reject the null hypothesis.

Conclusion:
Based on the sample of 250 respondents, at 5% level of significance, there is sufficient evidence to conclude that the spending before the campaign exposure is not the same as after for the population of the respondents.
QUESTION 6
H0: Positive, neutral and negative responses are equally likely amongst the population of Part-time workers.
H1: At least one of the responses is not equally likely amongst the population of Part-time workers.

Table 6(a): Chi-Square Goodness of Fit Test of NEWATT | | Observed N | Expected N | Residual | Positive | 42 | 37.7 | 4.3 | Neutral | 22 | 37.7 | -15.7 | Negative | 49 | 37.7 | 11.3 | Total | 113 | | |

Table 6(b): Test Statistics | | NEWATT | Chi-Square | 10.425a | df | 2 | Asymp. Sig. | .005 | a. 0 cells (0.0%) have expected frequencies less than 5. The minimum expected cell frequency is 37.7. |
The results show that: * The significant value of the Chi-square goodness of fit test is 0.005, which is smaller than 0.05, the level of significance for the test. Therefore, we reject the null hypothesis. * The significant value of 0.005 indicates that there is sufficient evidence from the sample to reject the null hypothesis.

Conclusion:
Based on the sample of 113 Part-time workers, at the 5% level of significance, there is sufficient evidence to conclude that at least one of the responses is not equally likely amongst the population of Part-time workers.

QUESTION 7
H0: Attitudes are independent of the method of media campaign that the respondents in the population are exposed to.
H1: Attitudes are dependent of the of media campaign that the respondents in the population are exposed to. Table 7(a): Crosstabulation of NEWATT * Media Campaign | | Media Campaign | Total | | TV | Radio | Newspaper | Internet | | NEWATT | Positive | Count | 22 | 25 | 14 | 24 | 85 | | | Expected Count | 19.4 | 22.4 | 20.1 | 23.1 | 85.0 | | Neutral | Count | 7 | 20 | 19 | 7 | 53 | | | Expected Count | 12.1 | 14.0 | 12.5 | 14.4 | 53.0 | | Negative | Count | 28 | 21 | 26 | 37 | 112 | | | Expected Count | 25.5 | 29.6 | 26.4 | 30.5 | 112.0 | Total | Count | 57 | 66 | 59 | 68 | 250 | | Expected Count | 57.0 | 66.0 | 59.0 | 68.0 | 250.0 |

Table 7(b): Chi-Square Tests of Independence | | Value | df | Asymp. Sig. (2-sided) | Pearson Chi-Square | 18.544a | 6 | .005 | Likelihood Ratio | 19.436 | 6 | .003 | Linear-by-Linear Association | 1.203 | 1 | .273 | N of Valid Cases | 250 | | | a. 0 cells (0.0%) have expected count less than 5. The minimum expected count is 12.08. |
The result shows that: * The significant value of the Chi-square test of independence is 0.005, which is smaller than 0.05, the level of significance for the test. Therefore, we reject the null hypothesis. * The significant value of 0.005 indicates that there is sufficient evidence from the sample to reject the null hypothesis.
Conclusion:
Based on the sample of 250 respondents, at 5% level of significance, there is sufficient evidence to conclude that attitudes are dependent of the of media campaign that the respondents in the population are exposed to.
QUESTION 8 Table 8: Crosstabulation of LOCATION * PRODUCT | | PRODUCT | Total | | Frozen | Households | Drinks | Health & Beauty | | LOCATION | Lower | Count | 12 | 2 | 2 | 8 | 24 | | | % within LOCATION | 50.0% | 8.3% | 8.3% | 33.3% | 100.0% | | | % within PRODUCT | 75.0% | 8.3% | 10.0% | 40.0% | 30.0% | | | % of Total | 15.0% | 2.5% | 2.5% | 10.0% | 30.0% | | Middle | Count | 0 | 12 | 10 | 8 | 30 | | | % within LOCATION | 0.0% | 40.0% | 33.3% | 26.7% | 100.0% | | | % within PRODUCT | 0.0% | 50.0% | 50.0% | 40.0% | 37.5% | | | % of Total | 0.0% | 15.0% | 12.5% | 10.0% | 37.5% | | Upper | Count | 4 | 10 | 8 | 4 | 26 | | | % within LOCATION | 15.4% | 38.5% | 30.8% | 15.4% | 100.0% | | | % within PRODUCT | 25.0% | 41.7% | 40.0% | 20.0% | 32.5% | | | % of Total | 5.0% | 12.5% | 10.0% | 5.0% | 32.5% | Total | Count | 16 | 24 | 20 | 20 | 80 | | % within LOCATION | 20.0% | 30.0% | 25.0% | 25.0% | 100.0% | | % within PRODUCT | 100.0% | 100.0% | 100.0% | 100.0% | 100.0% | | % of Total | 20.0% | 30.0% | 25.0% | 25.0% | 100.0% |

Out of 24 products at lower location, 50% is frozen product and 33.3% is health & beauty product. Out of 30 products at lower location, 40% is household product and 33.3% is drinks product. Out of 26 products at upper location, 38.5% is household product and 30.8% is drinks product.
Out of 16 which are frozen product, 75% is lower location and 25% is upper location. Out of 24 which are household products, 50% is middle location and 41.7% is upper location. Out of 20 which are drinks products, 50% is middle location, and 40% is upper location. Out of 20 which are health & beauty products, 40% is lower location and 40% is middle location.

QUESTION 9
H0: The mean sales are the same for all three display positions.
H1: At least one difference in mean sales according to display positions. Table 9: ANOVA Test for Sales | | Sum of Squares | df | Mean Square | F | Sig. | Between Groups | 646118764.455 | 2 | 323059382.228 | 37.303 | .000 | Within Groups | 666846934.295 | 77 | 8660349.796 | | | Total | 1312965698.750 | 79 | | | |

The test of effect of display position / the results show that: * The significant value of the 1-way ANOVA test for location is 0.000, which is smaller than 0.05, the level of significance for the test. Therefore, we reject the null hypothesis. * The significant value of 0.000 indicates that there is sufficient evidence to reject the null hypothesis.

Conclusion:
Based on the sample of 80 observations, at the 5 level of significance, there is sufficient evidence to conclude that at least one difference in mean sales according to display position.

QUESTION 10 Table 10: Post-hoc Multiple Comparisons & Tukey CI | (I) LOCATION | (J) LOCATION | Mean Difference (I-J) | Std. Error | Sig. | 95% Confidence Interval | | | | | | Lower Bound | Upper Bound | Lower | Middle | 6082.083* | 805.932 | .000 | 4156.02 | 8008.15 | | Upper | 6330.545* | 833.030 | .000 | 4339.72 | 8321.37 | Middle | Lower | -6082.083* | 805.932 | .000 | -8008.15 | -4156.02 | | Upper | 248.462 | 788.523 | .947 | -1636.00 | 2132.92 | Upper | Lower | -6330.545* | 833.030 | .000 | -8321.37 | -4339.72 | | Middle | -248.462 | 788.523 | .947 | -2132.92 | 1636.00 | *. The mean difference is significant at the 0.05 level. |

The results show that: * The significant value of Lower-Middle and Lower-Upper are 0.000, which is smaller than 0.05, the level of significance for the test. Therefore, the pairs of Lower-Middle and Lower-Upper have significantly different mean sales. * We are 95% certain that the mean sales difference for Lower-Middle is between $415, 602 and $800, 815 while, the means sales difference for Lower-Upper is between $433, 972 and $832, 137. * The mean sales of lower location is the highest among all locations, followed by middle location then upper location.

Conclusion:
At the 5% level of significance, there is sufficient evidence to conclude that the mean sales for lower location is significantly higher than the mean sales for middle and upper location.

QUESTION 11

1st hypothesis Ho: There are no interaction effects between product and promotion that affect sales.
HA: There are interaction effects between product and promotion that affect sales.

2nd hypothesis
Ho: The mean sales are the same for all products.
HA: At least one difference in means sales according to products.

3rd hypothesis
Ho: The mean sales are the same for all promotion methods.
HA: At least one different in means sales according to promotion.

Two-way ANOVA Test of Sales

Table 11: Tests of Between-Subjects Effects | Source | Type III Sum of Squares | df | Mean Square | F | Sig. | Corrected Model | 779533686.171a | 14 | 55680977.584 | 6.785 | .000 | Intercept | 3481547502.410 | 1 | 3481547502.410 | 424.235 | .000 | Productcategory | 243852666.442 | 3 | 81284222.147 | 9.905 | .000 | Promotion | 56436395.744 | 3 | 18812131.915 | 2.292 | .086 | Productcategory * Promotion | 330513036.514 | 8 | 41314129.564 | 5.034 | .000 | Error | 533432012.579 | 65 | 8206646.347 | | | Total | 5674694500.000 | 80 | | | | Corrected Total | 1312965698.750 | 79 | | | | a. R Squared = .594 (Adjusted R Squared = .506) |

Test of interaction effect: * The significance of the two-way ANOVA test between product and promotion is 0.000, which is smaller than the 0.05, the level of significance for the test. Therefore, we reject the 1st null hypothesis. * The significant value of 0.000 indicates that there is sufficient evidence to reject the null hypothesis.

Conclusion:
Based on the sample of 80 observations, at the 5% level of significance, there is sufficient evidence to conclude that there are interaction effects between product and promotion that affect sales.

Test of effect on product: * The significance of the two-way ANOVA test for promotion is 0.000, which is smaller than 0.05, the level of significance for the test. Therefore, we reject the 2nd null hypothesis. * The significant value 0.000 indicates that there is sufficient evidence to reject the null hypothesis.

Conclusion:
Based on the sample of 80 observations, at the 5% level of significance, there is sufficient evidence to conclude that there is at least one difference in mean sales according product.

Test of effect on promotion: * The significance of the two-way ANOVA test for promotion is 0.086, which is larger than 0.05, the level of significance for the test. Therefore, we do not reject the 3rd null hypothesis. * The significance value of 0.086 indicates that there is insufficient evidence to reject the null hypothesis.

Conclusion:
Based on the sample of 80 observations, at the 5% level of significance, we conclude that the mean sales are the same for all promotions methods.
QUESTION 12 Table 12 (a): Multiple Comparisons by Product | (I) PRODUCT | (J) PRODUCT | Mean Difference (I-J) | Std. Error | Sig. | 95% Confidence Interval | | | | | | Lower Bound | Upper Bound | Frozen | Households | 4711.46* | 924.586 | .000 | 2273.55 | 7149.37 | | Drinks | 3514.63* | 960.858 | .003 | 981.07 | 6048.18 | | Health & Beauty | 248.62 | 960.858 | .994 | -2284.93 | 2782.18 | Households | Frozen | -4711.46* | 924.586 | .000 | -7149.37 | -2273.55 | | Drinks | -1196.83 | 867.338 | .516 | -3483.80 | 1090.13 | | Health & Beauty | -4462.83* | 867.338 | .000 | -6749.80 | -2175.87 | Drinks | Frozen | -3514.63* | 960.858 | .003 | -6048.18 | -981.07 | | Households | 1196.83 | 867.338 | .516 | -1090.13 | 3483.80 | | Health & Beauty | -3266.00* | 905.905 | .003 | -5654.66 | -877.34 | Health & Beauty | Frozen | -248.62 | 960.858 | .994 | -2782.18 | 2284.93 | | Households | 4462.83* | 867.338 | .000 | 2175.87 | 6749.80 | | Drinks | 3266.00* | 905.905 | .003 | 877.34 | 5654.66 | Based on observed means. The error term is Mean Square(Error) = 8206646.347. | *. The mean difference is significant at the 0.05 level. |

Table 12a shows the 95% Tukey confidence interval for the mean difference between six pair of products categories.

The results show that:

* From the significance of the test, the pairs of Frozen-Household, Frozen-Drinks, Health & Beauty- Households and Health & Beauty- Drinks have significantly different means sales. * The significant value for Frozen-Household, Frozen-Drinks, Health & Beauty- Households and Health & Beauty- Drinks is 0.000, 0.003, 0.000 and 0.003 respectively, which is smaller than 0.05, the level of significance for the test. * * We are 95% certain that the mean sales difference between Frozen-Household is between $227,355 and $714,937, Frozen-Drinks is between $98,107 and $604,818, Health & Beauty- Households is between $217,587 and $674,980 and Health & Beauty- Drinks is between $87,734 and $565,466.

Conclusion:
At the 5% level of significance, there is sufficient evidence to conclude that the mean difference between Frozen-Household, Health & Beauty-Household, Frozen-Drinks and Health & Beauty-Drinks are significantly different. Besides, there is sufficient evidence to conclude that the mean sale for Frozen is significantly higher than the mean sales for Household and Drinks. Apart from that, there is also sufficient evidence to conclude that the mean sale for Health & Beauty is significantly higher than the mean sales for Household and Drinks.

Table 12 (b): Multiple Comparisons by Promotion | (I) PROMOTION | (J) PROMOTION | Mean Difference (I-J) | Std. Error | Sig. | 95% Confidence Interval | | | | | | Lower Bound | Upper Bound | Leaflet | Magazines | -1873.10 | 950.636 | .210 | -4379.69 | 633.50 | | Newspapers | 378.00 | 960.858 | .979 | -2155.55 | 2911.55 | | Internet | -1710.22 | 932.591 | .267 | -4169.24 | 748.80 | Magazines | Leaflet | 1873.10 | 950.636 | .210 | -633.50 | 4379.69 | | Newspapers | 2251.10 | 895.056 | .067 | -108.95 | 4611.14 | | Internet | 162.88 | 864.641 | .998 | -2116.97 | 2442.73 | Newspapers | Leaflet | -378.00 | 960.858 | .979 | -2911.55 | 2155.55 | | Magazines | -2251.10 | 895.056 | .067 | -4611.14 | 108.95 | | Internet | -2088.22 | 875.867 | .090 | -4397.67 | 221.23 | Internet | Leaflet | 1710.22 | 932.591 | .267 | -748.80 | 4169.24 | | Magazines | -162.88 | 864.641 | .998 | -2442.73 | 2116.97 | | Newspapers | 2088.22 | 875.867 | .090 | -221.23 | 4397.67 | Based on observed means.The error term is Mean Square (Error) = 8206646.347. |

Table 12b shows the 95% Tukey confidence interval for the mean difference between six pairs of promotional categories.

The results show that: * From the significance of the test, none of the pairs have significantly different mean sales. * The significance value of Leaflet-Newspapers is 0.979, Magazines-Leaflet is 0.210, Magazines-Newspapers is 0.067, Magazines-Internet is 0.998, Newspapers-Leaflet is 0.267and Internet-Newspapers is 0.090. These values are larger than 0.05, the level of significance for the test. * We are 95% certain that the mean difference between Leaflet and Newspapers sales is between -$215,555 and $291,155, the mean difference between Magazines and leaflet sales is -$63,350 and $437, 969, the mean difference between Magazines and Newspapers sales is -$10,895 and $461,114, the mean difference between Magazines and Internet sales is -$211, 697 and $244, 273, the mean difference between Newspapers and Leaflet and the mean difference between Internet and Newspapers sales is between -$22,123 and $439, 767.

Conclusion:
At the 5% level of significance, there is sufficient evidence to conclude that the mean sales for all promotion categories is not significant.

QUESTION 13

H0: The distributions of sales are the same for all three-display positions.
H1: At least one distribution of sales has a different display positions.

Table 13 (a): Ranks of Kruskal Wallis Test | | LOCATION | N | Mean Rank | SALES ('00s) | Lower | 24 | 60.92 | | Middle | 30 | 33.07 | | Upper | 26 | 30.23 | | Total | 80 | |

Table 13 (b): Test Statisticsa,b | | SALES ('00s) | Chi-Square | 26.683 | df | 2 | Asymp. Sig. | .000 | a. Kruskal Wallis Test | b. Grouping Variable: LOCATION |
The result shows that: * The significance of the Kruskall-Wallis test is 0.000, which is smaller than 0.05, the level of significance value of the test. * The significance value of 0.000 indicates that there is a strong evidence to reject the null hypothesis.

Conclusion:
Based on the sample of 80 observations, at the 5% level of significance, we can conclude that there is at least one of the distributions of sales is not the same for all three-display positions.

QUESTION 14

Table 14: Descriptive Statistics for Sales ($‘00s) | N | Valid | 80 | | Missing | 0 | Mean | 7383.88 | Std. Deviation | 4076.741 | Skewness | 1.260 | Std. Error of Skewness | .269 | Kurtosis | .647 | Std. Error of Kurtosis | .532 |

The results show that: * Skewness of descriptive statistic for sale is considerably larger than 0 * Kurtosis of descriptive statistic for sale is considerably larger than 0

Conclusion:
With the consideration of the results provided by skewness, kurtosis and histogram, it is shown that a Kruskal Wallis test seems safer than a One-Way ANOVA test.