This document contains solved answers related to Statistics for Business Decision Making. It includes topics like frequency distribution, regression, ANOVA, and estimated regression equation. The document provides step-by-step solutions to each problem.
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Running Head: STATISTICS FOR BUSINESS DECISION MAKING Statistics for Business Decision Making Name of the Student Name of the University Student ID
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1STATISTICS FOR BUSINESS DECISION MAKING Tableof Contents Answer 1....................................................................................................................................2 Answer 2....................................................................................................................................3 Answer 3....................................................................................................................................3 Answer 4....................................................................................................................................4
2STATISTICS FOR BUSINESS DECISION MAKING Answer 1 (a)The required frequency distribution table of the examination scores of 20 students with a class width of 10 is given in the following table: Examination score Freque ncy Relative frequency Cumulative frequency Cumulative relative frequency Percent frequency 50-6030.1530.1515 60-7020.150.2510 70-8050.25100.525 80-9040.2140.720 90-10060.320130 Total201100 (b)The required histogram showing the percent frequency distribution of the examination scores is given in the following figure: 50-6060-7070-8080-9090-100 0 5 10 15 20 25 30 35 Histogram (percent frequency distribution) Examination Scores Percent Frequency The histogram clearly shows that the examination scores of the students are negatively skewed. This indicates that there are more students who have secured marks that are higher than the average examination scores. This indicates that the number of students securing higher examination scores is more than the number of students securing lower examination scores.
3STATISTICS FOR BUSINESS DECISION MAKING Answer 2 ANOVA dfssmsFp value Regression1354.689354.6891.966220.003983 Residuals397035.262180.3913 Total40 CoefficientsStandard Error Intercept54.0762.358 X0.0290.021 (a)The sample size is given by the following formula: (Total df + 1) = 40 + 1 = 41 (b)Atα= 0.05, it can be said that unit price and demand are significantly related as the p- value obtained from the ANOVA table given is 0.004, which is less than the level of significance (α). (c)The coefficient of determination has been obtained as 0.048, which indicates that 4.8 percent of the variability in the supply of the product can be explained by the changes in the unit price of the product. (d)The coefficient of correlation between supply of the product and unit price of the product is 0.219. This indicates that there is a positive relationship between supply and unit price of the product. With the increase in the unit price of the products, the supply also increases. (e)The predicted supply (in units) is given by the following formula: Supply = 54.076 + (0.029 * 50) = 55.526 units = 56 units. Answer 3 (a)The required ANOVA table for testing the difference in the production between four different programs is given as follows:
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4STATISTICS FOR BUSINESS DECISION MAKING SUMMARY Groups CountSum Average Variance rogramAP5725145525 rogramPB5675135425 rogramCP5950190312.5 rogramDP5750150637.5 ANOVA Source of VariationSSdfMS FP-valueF crit etweenroupsBG875032916.6666676.1403510.005573.238872 ithinroupsWG760016475 Total1635019 (b)At 0.05 level of significance, it can be said that there are significant differences in the productivity of the four different types of programs as the p-value obtained from the ANOVA analysis is 0.006, which is less than the level of significance. The average productivity of Program C has been found to be the highest. Thus, the company will have increased productivity if Program C is adopted. Answer 4 (a)The estimated Regression equation is Sales (y) = 3.598 + (41.32 * Price) + (0.013 * Advertising) egressiontatisticsRS MultipleR0.878 RSquare0.771 AdjustedRSquare0.656 StandardrrorE1.837 bservationsO7 AVANO dfSSMSFignificanceSF Regression245.35322.6766.7170.053 Residual413.5043.376
5STATISTICS FOR BUSINESS DECISION MAKING otalT658.857 Coefficients tandarS d ErrorttatSP value- oerL w 95% pperU 95% oerL w 90.0% pperU 90.0% nterceptI3.5984.0520.8880.425-7.65314.848-5.04112.236 riceP41.32013.3373.0980.0364.29078.35012.88769.753 Advertising0.0130.3280.0400.970-0.8960.923-0.6850.712 (b)Atα= 0.10, the model is significant as the value of significance F is obtained to be 0.053, which is less than the level of significance (α). (c)At α= 0.10, competitors’ price is significantly related to Sales as the p-value obtained is 0.036, which is less than the level of significance. Advertising is not significantly related to Sales as the p-value obtained is 0.97, which is more than the level of significance. (d)By dropping the insignificant variable, Advertising, the re-estimated model is given by the following equation: Sales (y) = 3.58 + (41.6 * Price) egressiontatisticsRS MultipleR0.877761 RSquare0.770464 AdjustedRSquare0.724557 StandardrrorE1.643765 bservationsO7 AVANO dfSSMSFignificanceSF Regression145.3473345.3473316.783110.009385 Residual513.509812.701963 otalT658.85714 CoefficientstandarS d Error ttatSP value-oerL w 95% pperU 95% oerL w 90.0% ppeU r 90.0
6STATISTICS FOR BUSINESS DECISION MAKING % nterceptI3.583.610.990.37-5.6912.86-3.6910.85 riceP41.6010.164.100.0115.5067.7121.1462.07 (e)From the model estimated in part (d), it can be said that with one-unit increase in price, the sales will increase by 41.6 units.