Hi6007 Statistics Tutorial Solution Answers Assessment Answers
Below you are given the examination scores of 20 students (data set also provided in accompanying MS Excel file).
52 99 92 86 84
63 72 76 95 88
92 58 65 79 80
90 75 74 56 99
52 99 92 86 84
63 72 76 95 88
92 58 65 79 80
90 75 74 56 99
a. Construct a frequency distribution, cumulative frequency distribution, relative frequency distribution, cumulative relative frequency distribution and percent frequency distribution for the data set using a class width of 10. (5 marks)
b. Construct a histogram showing the percent frequency distribution of the examination scores. Comment on the shape of the distribution.
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).
a. What has been the sample size for this problem
b. Determine whether or not demand and unit price are related. Use α = 0.05. (2 marks) Determine whether or not demand and unit price are related. Use α = 0.05.
Compute the coefficient of determination and fully interpret its meaning. Be very specific.Compute the coefficient of correlation and explain the relationship between supply and unit price.
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).
a. What has been the sample size for this problem
b. Determine whether or not demand and unit price are related. Use α = 0.05. (2 marks) Determine whether or not demand and unit price are related. Use α = 0.05.
Compute the coefficient of determination and fully interpret its meaning. Be very specific.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). Program A Program B Program C Program D
150 150 185 175
130 120 220 150
120 135 190 120
180 160 180 130
145 110 175 175
a. Construct an ANOVA table.
b. 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).
Week Price Advertising Sales
1 .33 5 20
2 .25 2 14
3 .44 7 22
4 .40 9 21
5 .35 4 16
6 .39 8 19
7 .29 9 15
a. What is the estimated regression equation? Show the regression output.
b. Determine whether the model is significant overall. Use α = 0.10.
c. Determine if competitor’s price and advertising is individually significantly related to sales. Use α = 0.10. (2 marks)
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? Interpret the slope coefficient(s) of the model.
Answer:
| Examination scores | Classes | Frequency | Cumulative Frequency | Relative Frequency | Cumulative Relative Frequency | Percent Frequency | |||||||||
| 52 | > 57 | 2 | 2 | 0.1 | 0.1 | 10% | |||||||||
| 63 | 57 to 61 | 1 | 3 | 0.05 | 0.15 | 5% | |||||||||
| 92 | 61 to 66 | 2 | 5 | 0.1 | 0.25 | 10% | |||||||||
| 90 | 66 to 71 | 0 | 5 | 0 | 0.25 | 0% | |||||||||
| 99 | 71 to 76 | 4 | 9 | 0.2 | 0.45 | 20% | |||||||||
| 72 | 76 to 80 | 2 | 11 | 0.1 | 0.55 | 10% | |||||||||
| 58 | 80 to 85 | 1 | 12 | 0.05 | 0.6 | 5% | |||||||||
| 75 | 85 to 90 | 3 | 15 | 0.15 | 0.75 | 15% | |||||||||
| 92 | 90 to 94 | 2 | 17 | 0.1 | 0.85 | 10% | |||||||||
| 76 | < 94 | 3 | 20 | 0.15 | 1 | 15% | |||||||||
| 65 | Total | 20 | 99 | 1 | 4.95 | 1 | |||||||||
| 74 | |||||||||||||||
| 86 | |||||||||||||||
| 95 | |||||||||||||||
| 79 | |||||||||||||||
| 56 | |||||||||||||||
| 84 | |||||||||||||||
| 88 | |||||||||||||||
| 80 | |||||||||||||||
| 99 | |||||||||||||||
| ANOVA | |||||||||||||||
| df | SS | MS | F | Significance F | |||||||||||
| Regression | 1 | 354.689 | 354.689 | 1.966 | 0.169 | ||||||||||
| Residual | 39 | 7035.262 | 180.391 | ||||||||||||
| 40 | 7389.951 | ||||||||||||||
| Coefficients | Standard error | t stat | P value | ||||||||||||
| Intercept | 54.076 | 2.358 | 22.933 | 0.001 | |||||||||||
| X | 0.029 | 0.021 | 1.381 | 0.175 | |||||||||||
| Employee's output for a day's work | |||||||||||||||
| Program A | Program B | Program C | Program D | ||||||||||||
| 150 | 150 | 185 | 175 | ||||||||||||
| 130 | 120 | 220 | 150 | Anova: Single Factor | |||||||||||
| 120 | 135 | 190 | 120 | ||||||||||||
| 180 | 160 | 180 | 130 | SUMMARY | |||||||||||
| 145 | 110 | 175 | 175 | Groups | Count | Sum | Average | Variance | |||||||
| Program A | 5 | 725 | 145 | 525 | |||||||||||
| Program B | 5 | 675 | 135 | 425 | |||||||||||
| Program C | 5 | 950 | 190 | 312.5 | |||||||||||
| Program D | 5 | 750 | 150 | 637.5 | |||||||||||
| ANOVA | |||||||||||||||
| Source of Variation | SS | df | MS | F | P-value | F crit | |||||||||
| Between Groups | 8750 | 3 | 2916.667 | 6.140 | 0.006 | 3.239 | |||||||||
| Within Groups | 7600 | 16 | 475 | ||||||||||||
| Total | 16350 | 19 | |||||||||||||
| Weekly sales data | |||||||||||||||
| Week | Price | Advertising | Sales | ||||||||||||
| 1 | 0.33 | 5 | 20 | SUMMARY OUTPUT | |||||||||||
| 2 | 0.25 | 2 | 14 | ||||||||||||
| 3 | 0.44 | 7 | 22 | Regression Statistics | |||||||||||
| 4 | 0.4 | 9 | 21 | Multiple R | 0.8778 | ||||||||||
| 5 | 0.35 | 4 | 16 | R Square | 0.7706 | ||||||||||
| 6 | 0.39 | 8 | 19 | Adjusted R Square | 0.6558 | ||||||||||
| 7 | 0.29 | 9 | 15 | Standard Error | 1.8374 | ||||||||||
| Observations | 7 | ||||||||||||||
| ANOVA | |||||||||||||||
| df | SS | MS | F | Significance F | |||||||||||
| Regression | 2 | 45.3528 | 22.6764 | 6.7168 | 0.0526 | ||||||||||
| Residual | 4 | 13.5043 | 3.3761 | ||||||||||||
| Total | 6 | 58.8571 | |||||||||||||
| Coefficients | Standard Error | t Stat | P-value | Lower 95% | Upper 95% | Lower 95.0% | Upper 95.0% | ||||||||
| Intercept | 3.598 | 4.052 | 0.888 | 0.425 | -7.653 | 14.848 | -7.653 | 14.848 | |||||||
| Price | 41.320 | 13.337 | 3.098 | 0.036 | 4.290 | 78.350 | 4.290 | 78.350 | |||||||
| Advertising | 0.013 | 0.328 | 0.040 | 0.970 | -0.896 | 0.923 | -0.896 | 0.923 | |||||||
| SUMMARY OUTPUT | |||||||||||||||
| Regression Statistics | |||||||||||||||
| Multiple R | 0.8778 | ||||||||||||||
| R Square | 0.7705 | ||||||||||||||
| Adjusted R Square | 0.7246 | ||||||||||||||
| Standard Error | 1.6438 | ||||||||||||||
| Observations | 7 | ||||||||||||||
| ANOVA | |||||||||||||||
| df | SS | MS | F | Significance F | |||||||||||
| Regression | 1 | 45.3473 | 45.3473 | 16.7831 | 0.0094 | ||||||||||
| Residual | 5 | 13.5098 | 2.7020 | ||||||||||||
| Total | 6 | 58.8571 | |||||||||||||
| Coefficients | Standard Error | t Stat | P-value | Lower 95% | Upper 95% | Lower 95.0% | Upper 95.0% | ||||||||
| Intercept | 3.58 | 3.61 | 0.99 | 0.37 | -5.69 | 12.86 | -5.69 | 12.86 | |||||||
| Price | 41.60 | 10.16 | 4.10 | 0.01 | 15.50 | 67.71 | 15.50 | 67.71 | |||||||
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