The data in the table below presents the hourly quantity of production for three lines of…
HI6007
statistics for business DECISIONS
final assessmeNt
Trimester 1, 2022
Assessment Weight: 50 total marks
Instructions:
- All questions must be answered by using the answer boxes provided in this paper.
- Completed answers must be submitted to Blackboard by the published due date and time.
Please ensure you follow the submission instructions at the end of this paper.
Purpose:
This assessment consists of six (6) questions and is designed to assess your level of knowledge of the key topics covered in this unit.
Question 1 (7 marks)
The data in the table below presents the hourly quantity of production for three lines of production processes over the first 4 days in XYZ Company. Answer the questions based on the Excel Output given below.
Day | Process 1 | Process 2 | Process 3 |
1 | 33 | 33 | 28 |
2 | 30 | 35 | 36 |
3 | 28 | 30 | 30 |
4 | 29 | 38 | 34 |
ANOVA: Single Factor
SUMMARY
Groups | Count | Sum | Average | Variance |
Process 1 | 4 | 120 | 30 | 4.66667 |
Process 2 | 4 | 136 | 34 | 11.3333 |
Process 3 | 4 | 128 | 32 | 13.3333 |
ANOVA
Source of Variation | SS | df | MS | F | P value | |
Between Groups | 32 | ? | ? | ? | ||
Within Groups | 88 | ? | ? | |||
Total | 120 | 11 |
- State the null and alternative hypothesis for single factor ANOVA. (1 mark)
- State the decision rule (a = 0.05). (1.5 marks)
- Calculate the test statistic. (3 marks)
- Make a decision. (1.5 marks)
ANSWER: ** Answer box will enlarge as you type
Question 2 (7 marks)
Assume you have noted the following prices for books and the number of pages that each book contains.
Book | Price (in $) Y |
Pages X |
A | 7.00 | 500 |
B | 7.50 | 700 |
C | 9.00 | 750 |
D | 6.50 | 590 |
E | 7.50 | 540 |
F | 7.00 | 650 |
G | 4.50 | 480 |
A part of the output of a regression analysis of Y against X using Excel is given below:
SUMMARY OUTPUT | |||||||||||
Regression Statistics | |||||||||||
Multiple R | 0.75027 | ||||||||||
R Square | 0.56290 | ||||||||||
Adjusted R Square | 0.475487 | ||||||||||
Standard Error | 0.980614 | ||||||||||
Observations | 7 | ||||||||||
ANOVA | |||||||||||
df | SS | MS | F | Significance F | |||||||
Regression | 1 | 6.191972 | 6.191972 | ||||||||
Residual | 5 | 4.808028 | 0.961606 | ||||||||
Total | 6 | 11 | |||||||||
Coefficients | Standard Error | t Stat | P-value | ||||||||
Intercept | 1.04155 | 2.37717 | |||||||||
Pages | 0.00990 | 0.00390 | |||||||||
- State the estimated regression line and interpret the slope coefficient. (1 mark)
- What is the estimated total price when a book has 1000 pages? (1 mark)
- What is the value of the coefficient of determination? Interpret it. (1 mark)
- Test whether there is a significant relationship between price and pages at the 10% significance level. Perform the test using the following six steps. (4 marks)
Step 1. Statement of the hypothesis (0.5 mark)
Step 2. Standardised test statistic (0.5 mark)
Step 3. Level of significance (0.5 mark)
Step 4. Decision Rule (1 mark)
Step 5. Calculation of test statistic (1 mark)
Step 6. Conclusion (0.5 mark)
ANSWER:
Question 3 (11 marks)
A reporter for a student newspaper is writing an article on the cost of off-campus housing. A sample was taken of 10 one-bedroom units within a half-mile of the campus and the rents paid. The sample mean is $550 and the sample standard deviation is $60.05. We assume the population for one-bedroom units is normally distributed.
?Your task is to construct a 95% confidence interval for the average rent per month for the population by addressing the following:
- Parameter of interest (0.5 mark)
- Point estimator (0.5 mark)
- Sampling distribution of the point estimator (0.5 mark)
- Specify the formula for the 95% confidence interval estimator for the parameter
(1 mark)
- Perform the necessary calculations and write down the lower and upper limits of the confidence interval (3 marks)
- Interpret the calculated confidence interval (2 marks)
- Briefly explain what would happen to the width of the interval in each case: (i) the sample size increased, (ii) the sample standard deviation increased, and (iii) the level of confidence increased (3 marks)
ANSWER:
Question 4 (11 marks)
The following information has been collected on the sales of greeting cards for the past 6 weeks.
Week | Sales ($) |
1 | 85 |
2 | 90 |
3 | 95 |
4 | 110 |
5 | 105 |
6 | 115 |
- Develop a linear trend equation that can be used to forecast sales of greeting cards (6 marks)
- Use the linear trend equation developed in part A to forecast sales for week 7. (1 mark)
- Forecast the sales for week 7 using a three period weighted moving average with weights of 0.6 (week 6), 0.3 (week 5) and 0.1 (week 4). (2 marks)
- Compare and explain why the results in parts B and C are different. (2 marks)
ANSWER:
Question 5 (7 marks)
- In what situations do we use non-parametric tests and parametric tests? Explain with at least one example for each. ( 4 marks)
ANSWER a):
- Compare and contrast the scales on measurements used in statisics. Support your answer with examples. (3 marks)
ANSWER b):
Question 6 (7 marks)
For a particular range of cosmetics a filling process is set to fill tubs of face powder with 4 grams on average and standard deviation of 1 gram. A quality inspector takes a random sample of nine tubs and weighs the powder in each. The average weight of powder is 4.6 grams. What can be said about the filling process, with 95% level of confidence?
Step 1. Statement of the hypotheses (1 mark)
Step 2. Standardised test statistic formula (1 mark)
Step 3. Level of significance (0.5 mark)
Step 4. Decision Rule (Draw a bell to show rejection zone) (2 marks)
Step 5. Calculation of the statistic (1.5 marks)
Step 6. Conclusion (1 mark)
ANSWER:
END OF FINAL ASSESSMENT
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