This document contains solved assignments on frequency distribution, ANOVA, regression analysis and more for the course HI6007: Statistics For Business Decisions. It includes tables, histograms, ANOVA tables, regression tables and formulas.
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Running Head: HI6007: STATISTICS FOR BUSINESS DECISIONS HI6007: Statistics For Business Decisions Name of the Student Name of the University Student ID
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1HI6007: STATISTICS FOR BUSINESS DECISIONS Table of Contents Answer 1..........................................................................................................................................2 Part A...........................................................................................................................................2 Part B...........................................................................................................................................2 Part C...........................................................................................................................................3 Answer 2..........................................................................................................................................3 Part A...........................................................................................................................................3 Part B...........................................................................................................................................4 Part C...........................................................................................................................................4 Answer 3..........................................................................................................................................4 Answer 4..........................................................................................................................................5 Part A...........................................................................................................................................5 Part B...........................................................................................................................................5 Part C...........................................................................................................................................5 Part D...........................................................................................................................................6 Part E...........................................................................................................................................6
2HI6007: STATISTICS FOR BUSINESS DECISIONS Answer 1 Part A The following table shows the frequency, relative frequency and percent frequency of the furniture orders. Furniture Order ($)FrequencyRelative FrequencyPercent Frequency 100 - 15030.066% 150 - 200150.330% 200 - 250140.2828% 250 - 30060.1212% 300 - 35040.088% 350 - 40030.066% 400 - 45030.066% 450 - 50020.044% Grand Total501100% Part B The histogram in the figure below shows the distribution of the values of furniture orders. It can be seen from the shape of the histogram that the data is positively skewed.
3HI6007: STATISTICS FOR BUSINESS DECISIONS 100 - 150150 - 200200 - 250250 - 300300 - 350350 - 400400 - 450450 - 500 0% 5% 10% 15% 20% 25% 30% 35% Histogram showing the percent frequency of Furniture Order Values Furniture Order Values ($) Percent Frequency Part C For a positively skewed distribution, the most appropriate measure of location will be the median as in a positively skewed data, there are chances for the presence of outliers and the value of the median is unaffected with the presence of outliers. Answer 2 Part A The ANOVA table given below shows that the calculated F value is higher than the critical F value at 0.05 level of significance and with the degrees of freedom 1 and 46. Thus there exists significant relationship between demand (Y) and unit price (X). ANOVA dfSSMSFF-Critical Regression15048.8185048.81874.136854.051749 Residual463132.66168.10133 Total478181.479
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4HI6007: STATISTICS FOR BUSINESS DECISIONS Part B The coefficient of determination can be computed with the help of the following formula: R2=SS(Regression) SS(Total)=5048.818 8181.479=0.617 Thus, it can be said that 61.7 percent of the variability in demand can be explained by the independent variable unit price. Part C The coefficient of correlation (R) between demand and unit price can be computed as: R=√0.617=0.79 The correlation coefficient is showing very high value which indicates that there is a strong positive relationship between demand and unit price. Demand increases as the unit price increases. Answer 3 Source of VariationSum of Squares Degrees of Freedom Mean SquareFF- Critical Between Treatments390.582195.2925.8913.4668 Within Treatments (Error)158.4217.54 Total548.9823 The ANOVA table given above shows that the calculated value of F is higher than the critical F at 0.05 level of significance with 2 and 21 degrees of freedom. Thus, a significant difference exists between the three population.
5HI6007: STATISTICS FOR BUSINESS DECISIONS Answer 4 The completed regression table is presented in the following table: ANOVA dfSSMSFF-Critical Regression240.720.3580.1186.944 Residual41.0160.254 Total641.716 CoefficientsStandard Errort-statt-Critical Intercept0.8051 X10.49770.46171.07802.4469 X20.47330.038712.23002.446912 Part A The estimated regression equation relating Y to X1and X2is given as follows: Mobile Phones sold per day (y) = 0.8051 + (0.4977 * Price (in $1,000)) + (0.4733 * Number of advertising spots) Part B It can be seen from the ANOVA table that the calculated F is higher than the critical F at 0.05 level of significance with 2 and 4 degrees of freedom. Thus the regression model is significant. Part C Comparing the critical t value with the calculated t value for X1and X2, it can be seen that the calculated t value is less than critical t value for X1and hence, X1is insignificant. On the
6HI6007: STATISTICS FOR BUSINESS DECISIONS other hand, the calculated t value is more than critical t value for X2and hence, X2is significant. Thus, the coefficient of X2is significantly different from zero. Part D The slope coefficient of X2(0.4733) indicates that, with each unit increase in the number of advertising spots, the number of mobile phones sold per day increases by 0.4733. Part E If the company charges $20,000 for each phone and uses 10 advertising spots, then the number of mobile phones that is expected to be sold in a day is given by: Mobile Phones sold per day (y) = 0.8051 + (0.4977 * 20) + (0.4733 * 10) = 15.49~ 16. Thus, 16 mobile phones can be sold in a day.