Statistics for Economists 2
Study Abroad Assessment
| Department | School of Business |
| Module Code | EC1009 |
| Module Title | Statistics for Economists 2 |
| Number of Pages | 3 |
| Number of Questions | 4 |
| Instructions to Candidates | Answer ALL questionsEach question carries an equal markProvide full answers and show ALL your workings. Further instructions: The submission should be a single PDF file, and it can be either typewritten or handwritten. You must write your student ID number at the top of each page of your answers, and also provide page numbers. Do not write your name. It is your responsibility to ensure that the submitted file abides by the aforementioned instructions and that the electronic copy of your answers is legible. Marks will be deducted if the submitted file is not legible or if it does not abide by these instructions.You will submit electronically to the submission portal (Turnitin) which will become available on the Blackboard page of EC1009. |
Question 1 [25 marks]
A researcher is interested in the average weekly spending of a typical university student during the Easter holiday. A survey was sent out to 41 students in University A and it was found that the mean spending is £64 with a standard deviation of £10.
- [8 marks] Develop a 95% confidence interval for the population mean of weekly spending and interpret the confidence interval.
- [8 marks] What level of confidence is associated with an interval of 61.37 and 66.63 for the population mean of weekly spending?
- [9 marks] Another survey was sent out to 50 students in University B and it was found that the mean spending is £68 with a standard deviation of £9. We assume that the population variances are the same as the sample variances respectively for both universities. Construct a 90% confidence interval for the difference in average weekly spending in Universities A and B. Interpret your result.
Question 2 [25 marks]
- [3 marks] Explain the distinction between the null and alternative hypotheses.
- [11 marks] The manufacturer of a new toothpaste claims that at least eight out of ten dentists surveyed prefer their toothpaste and recommend it to their patients. An independent consumer research firm decides to test this claim. The findings in a sample of 400 dentists indicate that 76% do prefer this toothpaste. Is this evidence sufficient to doubt the manufacturer’s claim? Use
.
- [11 marks] A professional rock climber claims that he can climb a particular mountain within half an hour. From a random sample of 25 attempts, the rock climber averaged 33.3 minutes with a standard deviation of 3.9 minutes. Is there sufficient evidence to suggest that the climber’s claim is incorrect at a significance level of 10%?
Question 3 [25 marks]
- [12.5 marks] Students on a particular degree course are able to choose one of four optional modules to study in the final year of their course. In total 132 students are registered for this particular degree course this year. In previous years, Module A has been selected by 40% of the students, Module B by 30% of the students and Modules C and D have each been selected by 15% of the students. The student’s module selections for this year can be found in Table 1 (below). Does our data conform to the expected probabilities? Conduct the required test at the 1% significance level.
Table 1
| Module A | Module B | Module C | Module D | |
| Number of Students | 58 | 43 | 10 | 21 |
- [12.5 marks] The student’s choices are then categorised by their average grades from their second year of the degree course. We want to know if the module selection is dependent upon the average grade of the student. The calculated test statistic is 19.38. Explain (without recalculating) how the test statistic is obtained, stating any formulas used in the calculations. At the 5% significance level what can be concluded about the relationship between average grades and the module chosen?
Table 2
| Average Grade | Module A | Module B | Module C | Module D |
| 40-49% | 11 | 13 | 0 | 5 |
| 50-59% | 23 | 20 | 2 | 5 |
| 60-69% | 10 | 7 | 2 | 3 |
| 70+% | 14 | 3 | 6 | 8 |
Question 4 [25 marks]
Consider the following values of variables x and y:
| x | 97 | 113 | 81 | 68 | 90 | 79 |
| y | 103 | 103 | 105 | 115 | 127 | 104 |
- [15 marks] Use these data to develop an estimated regression equation where y is the dependent variable and x is the independent variable. Interpret the intercept and slope coefficient.
- [10 marks] Calculate the coefficient of determination
and interpret this result.
End of the Paper
