Question A (3 marks) A computer programmer claims that MacBooks using the Apple M1 chip are slower than MacBooks using the Intel chip. He wrote 10 programming scripts using R and ran each script on a MacBook witha M1 chip and a MacBook with an Intel chip. The time it took for each MacBook to execute the script is recorded in Excel file A2_macbook.xlsx. 1. Use the p-value approach to evaluate the computer programmer’s claim at the 10% signifi- cance level. Write down the five steps of hypothesis testing (use appropriate Excel functions to conduct you analysis but do not copy/paste a screenshot of your Excel output). Present your test statistic and p-value rounded to three decimal places. Question B (4 marks) A company is interested in how workers respond to wage cuts. The company formed 30 teams, each consisting of two employees, to sell coffee machines. All employees are paid the same daily wage initially. After a short period of time, teams were unknowingly randomly assigned to one of three pay-cut schemes (treatments). In treatment 1, one of the worker in the team receives a 25% pay cut while the other worker receives the same pay as before the treatment. In treatment 2, both workers in the team receive a 25% pay cut. In treatment 3, neither worker receives a pay cut. Excel file A2_sales.xlsx records the change in the number of coffee machines sold per day after the treatment. The company wants to know if the average change in the sales number differed depending on the which pay-cut scheme a team received. 1. Identify the sampling design. 2. Identify the dependent variable and the factor (the independent variable). Are these variables quantitative or qualitative? 3. Specify the null and the alternative hypothesis of interest to the company. 4. Specify the test statistic and its null distribution. 5. From this data, does the average change in sales number differ depending on which treatment the team received? Use a 1% significance level and the critical value approach for the test. Use appropriate Excel functions to conduct you analysis but do not copy/paste a screenshot of your Excel output. Present your test statistic and critical value rounded to two decimal places. Question C (4 marks) A gym consultant hypothesis that single people go to gym more often than married people. He surveyed 8 single people and 7 married people using the following questionnaire, where a score for each answer are given alongside the answer.
The answers from the 15 people are recorded in Excel file A2_gym.xlsx. Use the data to answer the following questions.
1. Identify the sampling design used by the consultant. 2. Do the data support the consultant’s hypothesis that single people go to gym more often than married people at the 5% level? Write down the five steps of hypothesis testing (use appropri- ate Excel functions to conduct you analysis but do not copy/paste a screenshot of your Excel output).
Question D (4 marks) Marketers are interested in how social media (e.g. Facebook and twitter) activity are related to the box office revenues of movies. Researchers collected the opening weekend box office revenue (in millions of dollars) for a sample of 23 recent movies. In addition, researchers obtained the tweet rate of each movie (average number of tweets referring to the movie per hour) in the week prior to the movie’s release. The data are recorded in Excel file A2_boxoffice.xlsx. Use EViews to answer the following questions. 1. Present a scatterplot of the data with the fitted line. 2. Write down a population linear regression model. 3. Use EViews to estimate the coefficients and write down the point estimate of the intercept and the slope coefficient (do not copy/paste EViews output).
4. 4. Write down the sampling distribution of the slope coefficient using the relevant statistics from EViews output. What assumptions are needed to obtain this sampling distribution?
5. 5. From the OLS estimates, how would the revenue change (on average) if the tweet rate increases by 50?