This document covers topics like histograms, regression, ANOVA, and more related to Statistics for Business Decisions. It includes calculations, tables, and graphs to help understand the concepts better. The document is suitable for students studying courses related to business statistics.
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Running Head: STATISTICS FOR BUSINESS DECISIONS Statistics for business decisions Name of the Student Name of the University Author Note
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1STATISTICS FOR BUSINESS DECISIONS Table of Contents Answer 1..........................................................................................................................................2 Part a............................................................................................................................................2 Part b............................................................................................................................................2 Answer 2..........................................................................................................................................2 Part a............................................................................................................................................2 Part b............................................................................................................................................3 Part c............................................................................................................................................3 Part d............................................................................................................................................3 Part e............................................................................................................................................3 Answer 3..........................................................................................................................................3 Part a............................................................................................................................................3 Part b............................................................................................................................................3 Answer 4..........................................................................................................................................4 Part a............................................................................................................................................4 Part b............................................................................................................................................4 Part c............................................................................................................................................4 Part d............................................................................................................................................5 Part e............................................................................................................................................5
2STATISTICS FOR BUSINESS DECISIONS Answer 1 Part a Class Width Frequenc y Cumulative Frequency Relative Frequenc y Cumulative Relative Frequency Percent Frequency 50 - 60330.150.1515% 70 - 60250.10.2510% 80 - 706110.30.5530% 90 - 804150.20.7520% 100 - 905200.25125% Part b 50 - 6070 - 6080 - 7090 - 80100 - 90 0% 5% 10% 15% 20% 25% 30% 35% Distribution of Scores Class Width Percentage Frequency The above image presents the histogram of Scores. From the histogram the scores seem to be normally distributed. Answer 2 dfSSMSFSignificance F Regression1354.689354.6891.966220.16876 Residual397035.262180.3913 Total407389.951 CoefficientsStandard Error Intercept54.0762.358 X0.0290.021
3STATISTICS FOR BUSINESS DECISIONS Part a The total sample size =dfRegression+dfResidual+1=1+39+1=41 Part b From the above calculation it is found that F(1,39) = 1.96622, Sig = 0.16876. Since sig- value is less than = 0.05 demand and unit price are not significantly related. Part c The coefficient of determination¿SSM SST=354.689 7389.951=¿0.048 From the value of coefficient of determination (r2) it can be said that 4.8% of the supply can be predicted from Unit Price. Part d The coefficient of correlation (r) =√0.048=0.219. From the value of coefficient of correlation (r) it is found that the correlation between unit price and supply is poor. Part e From the regression output the supply can be predicted as: Supply=54.076+0.029∗UnitPrice Thus, when unit price = $30,000 Supply=54.076+0.029∗50000=1504.076≈1504 Thus, the supply = 1504 thousands Answer 3 Part a Anova: Single Factor SUMMARY GroupsCountSumAverageVariance Program A5725145525 Program B5675135425 Program C5950190312.5 Program D5750150637.5 ANOVA Source of VariationSSdfMSFP-valueF crit Between Groups875032916.6676.1400.0063.239 Within Groups760016475 Total1635019
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4STATISTICS FOR BUSINESS DECISIONS Part b From the ANOVA table it is found that F(3,16) = 6.14, p-value = 0.006. Since p-value is less than = 0.05, hence there are statistically significant differences between programs. Answer 4 Part a The regression output of the model is given as: Regression Statistics Multiple R0.878 R Square0.771 Adjusted R Square0.656 Standard Error1.837 Observations7 ANOVA dfSSMSF Significance F Regression245.35322.6766.7170.053 Residual413.5043.376 Total658.857 Coefficients Standard Errort StatP-value Intercept3.5984.0520.8880.425 Price41.32013.3373.0980.036 Advertising0.0130.3280.0400.970 The regression equation is represented as: Supply=3.598+41.320∗Price+0.013∗Advertising Part b From the regression output F(2,4) = 6.717, sig = 0.053. Since sig (0.053) is less than = 0.10, hence both Price and Advertising together are significantly related to Sales. Part c From the regression output the p-value for Price = 0.036. Since p-value (0.036) is less than = 0.10, hence price individually related to sales. In addition, the p-value for Advertising = 0.970.Sincep-value(0.970)ismorethan =0.10,henceAdvertisingindividuallyis statistically not related to sales.
5STATISTICS FOR BUSINESS DECISIONS Part d Based on “part c” above Price is used to predict Sales. Regression Statistics Multiple R0.878 R Square0.770 Adjusted R Square0.725 Standard Error1.644 Observations7 ANOVA dfSSMSF Significance F Regression145.34745.34716.7830.009 Residual513.5102.702 Total658.857 Coefficients Standard Errort StatP-value Intercept3.5823.6080.9930.366 Price41.60310.1554.0970.009 The new estimated equation: Supply=3.582+41.603∗Price Part e The slope of the regression equation = 41.603. The slope of the regression equation can be interpreted as with unit increase in Price sales increases by 41.603 units.