1. The Delhi police are interested in determining the average speed of automobiles traveling on the Delhi-Agra Highway. To accomplish this task, the speed of every tenth car passing a particular point on the Delhi-Agra highway is recorded.
2. a. What is the population for this study?
3. b. What constitutes the sample?
4. c. Is speed a categorical or a quantitative variable?
5. d. If speed is categorical, what type of categorical? If speed is quantitative, what type of continuous?
6. e. What type of measurement scale is used?
7. 2. Compute the mean, median, and mode score if the following frequency distribution shows the Test scores of a sample of MBA-DFB students: Test Score Frequency 300 up to 400 2 600 up to 700 5 400 up to 500 6 700 up to 800 2 500 up to 600 10.
8. 3. A recent study reported the percentage of people 18 years of age and older who play football. Suppose that a study designed to collect new data on footballers and non-footballers uses a preliminary estimate of the proportion who play football of 0.30.
9. a. How large a sample should be taken to estimate the proportion of footballers in the population with a margin of error of .02? Use 95% confidence.
10. b. Assume that the study uses your sample size recommendation in part (a) and finds 520 footballers. What is the point estimate of the proportion of footballers in the population?
11. c. What is the 95% confidence interval for the proportion of footballers in the population.
12. 4. You are conducting a study on driving speed and Kilometers per liter for midsize automobiles. Using the following data: Speed (Km per Hour) 30 50 40 55 30 25 60 25 50 55 Km per Liter 28 25 25 23 30 32 21 35 26 25 Compute and interpret the sample correlation coefficient. Show your work in clear steps.
13. 5. Fifty percent of citizens believed the country was in a recession, even though technically the economic indicators have not yet confirmed this observation. For a sample of 20 citizens, make the following calculations.
14. a. Compute the probability that exactly 12 people believed the country was in a recession.
15. b. Compute the probability that no more than five people believed the country was in a recession.
16. c. How many people would you expect to say the country was in a recession?
17. d. Compute the variance and standard deviation of the number of people who believed the country was in a recession.
18. 6. During the period of time that a local restaurant takes phone-in bookings, calls come in at the rate of one every two minutes.
19. a. What is the expected number of calls in one hour?
20. b. What is the probability of no calls in a five-minute period?
21. 7. The exam scores of MBA students are normally distributed with a mean of 950 and a standard deviation of 200. (Also explain all your answers using Graphical work)
22. a) If your score was 1390. What percentage of students have scores more than You?
23. b) What are the minimum and the maximum values of the middle 87.4% of the scores?
24. c) If there were 165 students who scored above 1432. How many students took the exam?
25. 8. You are the new manager of a large supermarket. The company has adopted a few consumer-friendly policies and is using video clips to propagate the new policies. The following table provides data about the number of video clips shown on a randomly selected day and the sales turnover of the supermarket in the corresponding day. Days Number of Video Clips Shown Sales (in thousand rupees) 1 25 150 2 25 210 3 25 140 4 35 180 5 35 230 6 35 270 7 40 310 8 40 330 9 40 300 10 50 270 11 50 310 12 50 340.
26. a) Develop a simple regression model to predict the sales from the number of video clips shown.
27. b) Write down the obtained equation (using the variables Sales and Number of Videos) of the Simple Regression Line in this case. Did the estimated regression equation provide a good fit? Explain.
28. c) Explain the predicted behavior of the relationship between “Number of Videos” and “Sales” and provide any business insights to your company on the basis of your analysis. Also, predict what will happen to “Sales” if the company stops showing these “videos”?

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