1STATISTICS FOR BUSINESS DECISIONS Table of Contents ANSWER 1.....................................................................................................................................2 ANSWER 2.....................................................................................................................................5 ANSWER 3.....................................................................................................................................7 ANSWER 4...................................................................................................................................10 ANSWER 5...................................................................................................................................13
2STATISTICS FOR BUSINESS DECISIONS ANSWER 1 Part a The frequency table can be represented as: Class IntervalFrequencyRelative Frequency Percentage Frequency Distribution 15030.066.0% 200150.3030.0% 250140.2828.0% 30060.1212.0% 35040.088.0% 40030.066.0% 45030.066.0% 50020.044.0% Part b 150200250300350400450500 0.0% 5.0% 10.0% 15.0% 20.0% 25.0% 30.0% 35.0% Percentage Frequency Distribution of Order Value Frequency (Order Value) Percentage of Occurence Figure 1: Percentage Frequency Distribution of Order Value From the above histogram it is found that the order values are skewed to the right. Hence it can be said that the mean order value is greater than the median order value.
3STATISTICS FOR BUSINESS DECISIONS Part c Since the histogram is skewed right hence the mean order value is greater than the median order value. Thus the median of the order value would be a better measure of the data set. The median value of the order would represent the value below and above which 50% of the orders are. ANSWER 2 Anova dfSSMSFSignificance F Regressio n15048.8185048.81874.1370.000 Residual463132.66168.101 Total478181.479 Part a At 0.05 level of significance there is statistically significant relation between demand and unit price, p-value < 0.000. Part b The coefficient of determination¿SSM SST=5048.818 8181.479=0.617 Thus, 61.7% of the variability in demand can be predicted from Unit price. Part c The coefficient of correlation¿√0.617=0.786 From the value ofcoefficient of correlation, it can be said that there is a very strong correlation between demand and unit price.
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4STATISTICS FOR BUSINESS DECISIONS ANSWER 3 ANOVA Source of Variation Sum of Squares Degrees of Freedom Mean SquareFSignificance F Between Treatments390.5802195.29025.8910.000 Within Treatments (Error)158.400217.543 Total548.98023 dfBetween Treatments = 3 – 1 = 2Number of Treatments = 3 dfWithin Treatments = 23 – 2 = 21 MSM=SSM df=390.580 2=195.290 MSE=SST df=158.400 21=7.543 F=MSM MSE=195.290 7.543=25.891 Significance F is calculated in MS Excel by the formula =F.DIST.RT(25.891,2,21) At 0.05 level of significance, there is statistically significant difference among the means of the three populations, p-value < 0.000. ANSWER 4 Part a The relation of Y to X1 and X2 can be presented as: Y = 0.8051 + 0.4977*X1+ 0.4733*X2
5STATISTICS FOR BUSINESS DECISIONS Part b ANOVA dfSSMSFSignificance F Regression140.70040.700480.7090.000 Residual121.0160.085 1341.716 From the above calculations, it is found that there is statistically significant relation between the independent and dependent variables, p-value < 0.000 at 0.05 level of significance. Part c CoefficientsStandard Errort stat Intercept0.8051 X10.49770.46171.078 X20.47330.038712.230 t-stat for X1¿0.4977 0.4617=1.080 t-stat for X2=0.4733 0.0387=12.230 The tabulated t-value at 0.05 level of significance and 13 degrees of freedom is 2.16 Since, the t-stat is less than the tabulated value for Price (1.078 < 2.16), hence, the value of Price (X1) is significantlynotdifferent from zero. Since, the t-stat is more than the tabulated value for Advertising spots (12.230 > 2.16) hence the value of Advertising Spots (X2) is significantly different from zero.
6STATISTICS FOR BUSINESS DECISIONS Part d The slope coefficient for X2can be interpreted as: When the Price remains constant an increase in unit Advertising Spot would lead to an increase in mobile phone sold by 0.4733. Part e Charge = $20,000 = $20 x 1000 Advertising spots = 10 Y = 0.8051 + 0.4977*X1+ 0.4733*X2 Y = 0.8051 + 0.4977*20 + 0.4733*10 = 15.4921 Thus, number of mobile phones sold per day = 15.4921≈16