Statistics: ANOVA, Regression Analysis and Hypothesis Testing
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This article covers ANOVA, Regression Analysis and Hypothesis Testing in Statistics. It includes frequency distribution, histogram, ANOVA output, hypothesis testing, correlation coefficient, regression model, slope coefficient, and more.
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Question 1 (a)Frequency distribution (b)Histogram Comment: It can be seen from the above histogram that examination score does not exhibit normal distribution as it does not possess a bell curve. Further, a non-normal distribution is confirmed from the presence of negative skew. It is also evident from the shape of histogram that scores show significant deviations(Fehr and Grossman, 2013). 1
Question 2 Variables Supply (Y): Dependent variable Unit price (X): Independent variable ANOVA Output (a)Sample size = Degree of freedom + 1 = (1+39) +1 = 41 (b)Null and alternative hypothesis Slope coefficient (Unit price) = 0.029 Standard error (Unit price) = 0.021 Thevalueoftstat=(0.029 0.021)=1.381 Hypothesis test = Two tailed The p value =¿TDIST(1.38,39,2)=0.175 2
Given significance level = 5% Fail to reject null hypothesis because p value is greater than significance level. Unit price and supply is not associated (Harmon, 2016). (c)Coefficient of determination R2=SSR SST=354.68 (354.689)+(7035.262)=354.68 7389.95=0.048 Only 4.8% changes in supply would be offered explanation by change in unit prices. The percentage is quite low and thus, the regression model would not be a good fit for analysis (Hair, et.al., 2015). (d)Correlation coefficient R=¿ Only positive value ofcorrelation coefficientwould be taken as the sign of slope is positive. Further, the strength of association between unit price and supply is weak only as the value is lower than 0.5. (e)Supply units for $50,000 unit prices. Regression equation Thus, supply will be 55526 units for $50,000 unit prices. 3
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Question 3 (a)ANOVA Table (b)Hypothesis testing Test statistic (F value) = 6.140 The p value = 0.006 Significance level = 5% Reject the null hypothesis as p value is lower than significance level (0.006<0.05).Therefore, sufficient witnesses are present to make the conclusion that at least one of the group mean would be different (Harmon, 2016). 4
Question 4 (a)Regression model by considering sales as dependent variable andproduct price and advertising as independent variable. (b)Hypothesis testing Test statistic (F value) = 6.7168 5
The significance F = 0.0526 Significance level = 0.10 Reject the null hypothesis as significance F is lower than significance level (0.0526<0.1). Therefore, sufficient evidence is present to make the conclusion that the above model is significant. (c)Hypothesis testing For Price Null hypothesis H0:βprice=0 Alternative hypothesis H1:βprice≠0 Test statistic (t value) = 3.098 The p value = 0.036 Significance level = 0.01 Reject the null hypothesis as p value is lower than significance level (0.036<0.1).Therefore, sufficient evidence is present to make the conclusion that the slope coefficient (price) is significant. For Advertising Null hypothesis H0:βAdvertising=0 Alternative hypothesis H1:βAdvertising≠0 Test statistic (t value) = 3.098 The p value = 0.970 Significance level = 0.1 6
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Fail to reject the null hypothesis as p value is greater than significance level (0.970>0.01). Therefore, sufficient evidence is present to make the conclusion that the slope coefficient (advertising) is not significant (Flick, 2015). (d)Advertising: Insignificant variable and thus, can be taken away for the new model. (e)Slope coefficient = 41.60 It implies that sales would be increased by 41.60 units when there is an increase in the price by 1 unit. Reference 7
Fehr, F. H. and Grossman, G. (2013)An introduction to sets, probability and hypothesis testing. 3rd ed. Ohio: Heath. Flick, U. (2015)Introducing research methodology: A beginner's guide to doing a research project.4th ed. New York: Sage Publications. Hair, J. F., Wolfinbarger, M., Money, A. H., Samouel, P., and Page, M. J. (2015)Essentials of business research methods.2nd ed. New York: Routledge. Harmon, M. (2016)Hypothesis Testing in Excel - The Excel Statistical Master.7th ed. Florida: Mark Harmon. 8