Statistics Study Material with Solved Assignments and Dissertation - Desklib
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Question 1 (a)The frequency distribution of the examination scores (b)Histogram for representing the examination scores percentage The relevant observations can be extracted from the above highlighted histogram that the shape of histogram is not bell-curve which is indicative of non-normal distribution of examination 1
score. Further, high deviation has also been observed in data which is evident negative skew. Therefore, the distribution of examination score would not be assumed to be normal distributed (Flick, 2015). Question 2 (a)Unit price is represented as x and supply is represented as y. ANOVA table Normal and formula view (a)The sample size = 1 + (Degree of freedom) = 1 + (36+1) = 41 (b)Null and alternative hypothesis 2
Slope coefficient =0.029 The p value = 0.175 Significance level = 5% or 0.05 Visibly, the p value is more than significance level and hence, null hypothesis will not be rejected. Therefore, the variables supply and unit prices are not correlated (Flick, 2015). (c)R square Sum of squares regression= 354.689 Sum of squares of error = 7035.262 Total sum of squares = (354.689)+(7035.262) = 7389.95 Now, R square (Coefficient of determination) = Sum of squares regression/ Total sum of squares = 0.048 or 4.8% R square is indicates that that 4.8% deviation in supply will be described by deviation in unit price. This percentage is quite insignificant (low) and hence, the regression model does not constitute as good fit model (Harmon, 2016). (d)R The square root of coefficient of determination is termed as correlation coefficient. The sign of the correlation coefficient is decided based on the sign of slope coefficient. It is apparent that slope is position and therefore, the coefficient of correlation would also be positive (Hair, et.al., 2016). R = 0.219 3
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The value of R is inferior than 0.5 and therefore, the correlation strength between supply and unit price is not strong and would be assumed to be weak only (Harmon, 2016). (e)The regression line equation can be written as highlighted below. 4
Question 3 ANOVA single factor test output 5
Question 4 (a)The description of variables and regression output 6
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Regression equation Y=3.598+(41.320X1)+(0.013X2) (b)Hypothesis testing for regression model 7
(c)Hypothesis testing for slopes Relevant part of regression Significance level (Alpha) = 0.10 Slope coefficient: Price (X1) Observation: The p value < level of significance (0.036 <0.1) Result: “Reject the null hypothesis and accept alternative hypothesis (Flick, 2015).” 8
Summary:“Price is significant for the regression model. It means that statistically sale is correlated with the price.” Slope coefficient: Advertising Expenditure (X2) Observation: The p value > level of significance (0.97 >0.1) Result: “Fails to reject the null hypothesis and hence, cannot accept alternative hypothesis (Harmon, 2016).” Summary: “Advertising expenditure is insignificant for the regression model.” (d)Insignificance variable =Advertisingexpenditure Regression model only with statistically significant variable Regression equation Y=3.582+(41.603X1) 9
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(e)Interpretation of slope: The slope coefficient implies that change in sales to the tune of 41.60 units can be produced by a unit change in price. Further, the direction of change for both variables would be same as slope is positive. 10
Reference 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. (2016)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. 11