Hi6007 Group Assignment Faculty Of Assessment Answers
Question 1
Below you are given the examination scores of 20 students (data set also provided in accompanying MS Excel file).
Question 2
Shown below is a portion of a computer output for a regression analysis relating supply (Y in thousands of units) and unit price (X in thousands of dollars).
- What has been the sample size for this problem?
- Determine whether or not demand and unit price are related. Use α = 0.05. Determine whether or not demand and unit price are related. Use α = 0.05.
c.Compute the coefficient of determination and fully interpret its meaning. Be very specific.
d.Compute the coefficient of correlation and explain the relationship between supply and unit price.
Question 3
Allied Corporation wants to increase the productivity of its line workers. Four different programs have been suggested to help increase productivity. Twenty employees, making up a sample, have been randomly assigned to one of the four programs and their output for a day's work has been recorded. You are given the results below (data set also provided in accompanying MS Excel file).
- Construct an ANOVA table.
- As the statistical consultant to Allied, what would you advise them? Use a .05 level of significance.
Question 4
A company has recorded data on the weekly sales for its product (y), the unit price of the competitor's product (x1), and advertising expenditures (x2). The data resulting from a random sample of 7 weeks follows. Use Excel's Regression Tool to answer the following questions (data set also provided in accompanying MS Excel file).
- What is the estimated regression equation? Show the regression output.
- Determine whether the model is significant overall. Use α = 0.10.
- Determine if competitor’s price and advertising is individually significantly related to sales. Use α = 0.10.
Based on your answer to part (c), drop any insignificant independent variable(s) and re-estimate the model. What is the new estimated regression equation?
Answer:
Question 1
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).
Question 2
Variables
Supply (Y): Dependent variable
Unit price (X): Independent variable
- Sample size = Degree of freedom + 1 = (1+39) +1 = 41
- Null and alternative hypothesis
Slope coefficient (Unit price) = 0.029
Standard error (Unit price) = 0.021
Hypothesis test = Two tailed
The p value =
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).
- Coefficient of determination
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).
- Correlation coefficient
Only positive value of correlation coefficient would 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.
- Supply units for $50,000 unit prices.
Regression equation
Thus, supply will be 55526 units for $50,000 unit prices.
Question 3
- 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).
Question 4
- Hypothesis testing
Test statistic (F value) = 6.7168
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.
- Hypothesis testing
For Price
Null hypothesis H0:
Alternative hypothesis H1:
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:
Alternative hypothesis H1:
Test statistic (t value) = 3.098
The p value = 0.970
Significance level = 0.1
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).
- 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
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.
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