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QBA201 Quantitative Business Analysis

Homework Assignment 4

Spring 2020

Instructions:

The due date for this homework assignment is on Monday, May 4 at 5 pm. Assignments received after that time will be marked as late with a penalty of 10 points until the end of that day. Any assignments not received by the end of the day will receive a grade of 0.

You may use a Word processor to type and upload it as is. If you submit handwritten answers, make sure that your submission is neat, legible and professional in appearance. If you handwrite, you can scan and upload it as ONE pdf file on ilearn. Please note that it is your responsibility to make sure that you can upload it correctly and in the correct order with your name, ID and section number (Section 4, 5 or 6) written on the top of each page. Finally, show your work for all questions to receive full credit.

(10 points) Suppose Carrefour surveys 250 randomly selected customers to determine if they spend more than AED 500 per week on groceries. Of the 250 surveyed, 49 reported yes – they spend more than AED 500 per week on groceries. Using a 90% confidence level, compute a confidence interval estimate for the true proportion of customers who spend more than AED 500 per week on groceries.

(10 points) Use the data file “Trees” for this question. Christmas holiday celebrators in UAE face an important decision: buy a real or an artificial tree? A sample of 1508 male and female respondents age 18 years and older was interviewed. Respondents were asked whether they preferred a real (1) or artificial (2) tree. Do the data allow us to conclude at 1% significance level that more than 58% of all Christmas celebrators in UAE prefer artificial trees?

(10 points) A life insurance representative believes that the mean age of people who buy their first life insurance plan is less than 35. To test his belief he takes a random sample of 15 customers who have just purchased their first life insurance. Their ages are 42, 43, 28, 34, 30, 36, 25, 29, 32, 33, 27, 30, 22, 37, and 40. Can we conclude at the 1% significance level that the insurance representative is correct?

(10 points) Use the data file “income” for this question. In a survey of 80 randomly selected companies, presidents of the companies were asked report their annual income. Assuming the incomes are normally distributed with a standard deviation of $250,000, determine the 90% confidence interval estimate of the mean annual income of all company presidents.

(10 points) Past experience indicates the monthly long distance telephone bill is normally distributed with a mean of $17.85 and a standard deviation of $3.87. After an advertising campaign aimed at increasing long-distance telephone usage, a random sample of 25 household bills was taken. If we assume that the distribution of telephone bills is unchanged, can we conclude at 10% significance level that the campaign was successful?

19.61

20.14

19.57

19.26

14.03

19.24

15.98

24.85

26

19.46

18.29

16.91

26.15

19.64

16.75

20.52

25.47

18.19

12.56

28.47

14.13

19.72

17.05

13.92

12.38

(10 points) An electronics retailer is interested in studying the incomes of consumers in a particular area. The population standard deviation is known to be $1,000. What sample size would the researcher need to use for a 95% confidence if the margin of error should not be more than $50? What sample size would the researcher need to use for a 99% confidence if the margin of error should not be more than $60?

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(10 points) Use data file “remotes” for this question. A company that produces universal remote controls wanted to determine the number of remote control devices French homes contain. The company hired a statistician to survey 240 randomly selected homes and determine the number of remote controls. If there are 1 million households, estimate with 99% confidence the total number of remote controls in France.

(15 points). Ajmal perfumes is considering to open a kiosk at a certain location in Mall of the Emirates. Based on financial analyses, opening a kiosk is profitable only if the number of customers passing the location averages more than 25 per hour. The number of customers was observed for each of 30 different one-hour periods. The average number of customers was then recorded to be 26. Assume that the population standard deviation is known to be 4.

a. State the null and alternative hypotheses.

b. Can we conclude at the 5% significance level that the location is acceptable? How do you know?

c. Please state which type of error (Type I or Type II) may be committed here? Consider your conclusion in part (b) of this question and explain your answer. Also, what are the implications of committing such error?

(15 points) Freedom Pizza advertises that they deliver your pizza in less than 15 minutes of placing an order or it is free. A sample of 25 customers is selected at random. The average delivery time in the sample was 13 minutes with a sample standard deviation of 4 minutes.

If the delivery time is normally distributed,

a. State the null and alternative hypothesis.

b. Test to determine if we can infer at the 5% significance level that the population mean delivery time is less than 15 minutes.

c. Explain the results you find.

Christmas holiday celebrators in UAE - Business Analysis

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