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ECON20003 – QUANTITATIVE METHODS 2

Second Semester, 2022

Assignment 1

Exercise 2 (52 marks = 6 + 6 + 11 + 4 + 12 + 13)

The sales manager of the Happy Life company keeps records of the time her  salespeople spend on customer calls. She has found that salespeople who spend more time per customer call are more successful and that the most successful salespeople spend, on average, more than 50 minutes on a customer call. In order to see whether a new salesperson might become one of the firm’s most successful salespeople, the sales manager recorded the time (in minutes) this salesperson spent on a random sample of 35 calls during his probation period. These observations are saved in the a1e2.xlsx Excel file.

(a) (6 marks)

Consider the time variable and answer the following questions. Is this 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 a1e2. Import the data set from the a1e2 Excel data file to RStudio and save it as a1e2.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) (11 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 amounts of time the new salesperson spent on customer calls? Provide a precise interpretation of each of these statistics.

(d) (4 marks)

Construct a 95% confidence interval for the population mean of time the new salesperson spends on customer calls. Interpret your confidence interval.

(e) (12 marks)

Perform an appropriate test at the 5% significance level on the sample data to see whether the new salesperson might become one of the firm’s most successful salespeople. Specify the null and alternative hypotheses, the observed test statistic, make a statistical decision based on the p-value, and draw an appropriate conclusion.

(f) (13 marks)

What conditions are required to validate the confidence interval and the test in parts (d) and (e)? Are they likely satisfied? Use as much evidence as you can to support your answers.

 Exercise 3 (32 marks = 4 + 12 + 16)

The population of adolescent laborers who dropped out of high school at age 16 has a median reading comprehension score of 60 on a scale 0, 1, 2, …, 100. Suppose we would like to know whether adolescents still in school at age 16 achieve a higher median score on the same test than dropouts employed as laborers. To answer this research question, we took a random sample of 21 adolescents who are still in school at age 16 and recorded their scores on the same test. These scores are saved in the a1e3.xlsx Excel file. Perform all required calculations and tasks with RStudio / R.

(a) (4 marks)

Granted that the required conditions are satisfied, which tests can be used to answer the research question? Explain your answer.

(b) (12 marks)

Perform the tests you nominated in part (a) at the 5% significance level. For each test specify the null and alternative hypotheses, the observed test statistic, make a statistical decision based on the p-value, and draw an appropriate conclusion.

(c) (16 marks)

What conditions are required to validate the tests you performed in part (b)? Are they likely satisfied this time? Which test do you think is the best this time? Explain your answers and provide as much evidence as you can.