ECON20003 – QUANTITATIVE METHODS 2 First Semester, 2022 Assignment 1
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ECON20003 – QUANTITATIVE METHODS 2
First Semester, 2022
Assignment 1
In a work study exercise for a seaside hotel at a popular holiday destination in France a manager observed the following two variables for 50 randomly selected customers in June 2019:
Time: time, in seconds, taken to compile the bill of the customer.
Weekend: whether the bill was issued on a weekend or public holiday (1: Yes) or not (0: No).
These data are saved in the a1e1.xlsx Excel file.
(a) (6 marks)
Consider each variable and answer the following questions. Is the variable qualitative or quantitative? If it is qualitative, is it ranked or unranked? If it is quantitative, is it discrete or continuous? What is its level of measurement? Explain your answers.
(b) (6 marks)
Launch RStudio, create a new RStudio project and script, and name both a1e1. Import the data set from the a1e1 Excel data file to RStudio and save it as a1e1.RData. Attach the data to your RStudio project. Take now a screenshot of
your RStudio window and paste it into your assignment.
Perform the following tasks with RStudio / R.
(c) (12 marks)
For each variable illustrate (i) the frequency distribution and (ii) the relative frequency distribution of the sample data with a bar plot or with a histogram, whichever is more appropriate. In each case explain your choice. Customize every plot by adding a descriptive title and label to it, and by colouring it.1 Briefly describe what these plots tell you about this sample of times taken to compile the bills.
(d) (13 marks)
Obtain the smallest observation, the largest observation, the range, the 1st quartile, the median, the 3rd quartile, the mean, the standard deviation, and the coefficient of variation for Time. What do these statistics tell you about the compilation times of bills in this sample. Provide a precise interpretation of each of these statistics.
(e) (7 marks)
Construct a 90% confidence interval for the mean time taken to compile the bills of all customers in this hotel in June 2019. Interpret your confidence interval.
(f) (12 marks)
Perform a t-test at the 5% significance level to find out whether it is possible to conclude from these sample data that on average it takes less than 4.5 minutes to compile the bills of all customers in this hotel in June 2019. Specify the null and alternative hypotheses, the observed test statistic, make a statistical decision based on the p-value, and draw an appropriate conclusion. What if the level of significance is reduced to 1%? What if the level of significance is increased to 10%?
(g) (15 marks)
What conditions are required for the confidence interval and the t-test in parts (e) and (f), respectively? Are they likely satisfied? Use as much evidence from parts (c) and (d) as you can to support your answer.
(h) (24 marks)
To be safe, it is a good idea to double check the conclusions drawn in part (f) by running a nonparametric test as well. Which nonparametric tests can be used this time? Check whether the required conditions are satisfied and nominate the most appropriate test. Explain your choice. Perform this test. Do not forget to specify the null and alternative hypotheses, to report the observed test statistic, to make statistical decisions based on the p-value at the 5%, 1%, and 10% significance levels, and to draw appropriate conclusions.
(i) (5 marks)
Compare the conclusions you arrived at in parts (f) and (h). Be precise.
2022-03-27