Eynesbury: Quantitative Methods for Business Assignment.

Question 1-

Your colleagues have undertaken a study of personal income with data provided by a random survey of 300 employees in metropolitan Adelaide by asking "how much money did you earn last financial year?" They found that the mean income is $41,000; the median is $35,000; and the highest and lowest incomes are $250,000 and $2,400, respectively.

(a) Was the survey technique appropriate? What type of variable was being collected?  Fully explain.

(b) Determine if the distribution of income is symmetric, right- skewed or left-skewed?  How many people in the sample earned less than $35,000? Fully explain how you know.

(c) Based on the information supplied, can you determine how many families earned more than $41,000? Why or why not?

Question 2-

Three entrepreneurs have opened KidsKorner Toys, a shop selling high-quality toys.  Items are consigned to the shop by individuals who then receive a percent of the selling price of their items. Daily data for November 2014 is shown in Sheet1 of the Excel file called Assignment2.xls (available from the Assignments page of the course website).  The data consists of each day's gross sales, broken down by the method of payment (cash or credit card). 'Gross sales' in retailing are overall dollar sales, not adjusted for returns or discounts. The data record the number of items sold and the dollar amount of gross sales for each payment method on the day. The three owners of KidsKorner Toys expect credit card purchases to differ from cash purchases. You are requested to examine the distributions of the sale amounts for these two payment methods to see if this is indeed the case.

(a) Make a histogram and obtain Descriptive Statistics, including Quartile 1 and Quartile 3, for gross cash sales and for gross credit card sales.

EXCEL Instructions: Add your ID to the column names for gross cash and gross credit card sales (Gross-Cash should become Gross- Cash bloggsj001 etc). Please use the bins given in Sheet1 of Assignment 2.xls. Please make sure that the title of your histogram ends with your network ID (e.g. Histogram of gross cash sales bloggsj001). Ensure you conform with all rules of good chart presentation.

(b) Describe the shape (symmetry, modality and outliers) of each distribution.

(c) Nominate appropriate summary measures for the distribution of gross cash sales, and for the distribution of gross credit card sales. Give reason(s) for your choice.  For each distribution, give and interpret the values of the summary measures you have chosen.

Note: In order to achieve full marks for this question it is essential that you fully explain what you are doing, why you are doing it and the steps involved in providing a final solution. Ensure your answer is not just a set of calculations as 25% of the marks for this question are set aside for your explanation.

Question 3-

Six hundred investors were surveyed to determine whether a person who uses a full-service stockbroker has better performance in his or her investment portfolio than one who uses a discount stockbroker. In general, discount brokers offer no investment advice to their clients, whereas full-service brokers offer help in selecting stocks but charge larger fees. The data, based on the last 12 months, are summarized in the table below. Answer the questions that follow. In each case show the calculation and interpret your answer in words.

(a) What is the probability that an investor uses a full-service stockbroker?

(b) What is the probability that an investor's portfolio increases in value?

(c) What is the probability that an investor uses a discount stockbroker and the value of his or her portfolio increases?

(d) Suppose an investor uses a full-service stockbroker. What is then the probability that his or her portfolio increases in value?

(e) Suppose that an investor's portfolio increases in value. What is then the probability that this investor uses a discount stockbroker?

(f) Are 'type of broker' and 'portfolio value' independent or dependent? How do you know? Show calculations that support your answer.

Note: In order to achieve full marks for this question it is essential that you fully explain what you are doing, why you are doing it and the steps involved in providing a final solution. Ensure your answer is not just a set of calculations as 25% of the marks for this question are set aside for your explanation.

Question 4-

Employers may ask job applicants to take an IQ test because the test has been shown to predict performance on the job. One such test is the Wechsler Adult Intelligence Scale (WAIS). Scores on the WAIS for a 20 to 34 age group are approximately normally distributed with mean 110 and standard deviation 25.

(a) What proportion of people in this age group have scores above 160 and hence 'exceptional' intelligence? Use an appropriate diagram to assist to describe the proportion.

(b) Suppose that an employer examines WAIS test scores of 20 randomly chosen job applicants from this age group. What is the probability that the average test score in this sample is below 120? Use a diagram to assist in your explanation!

Note: In order to achieve full marks for this question it is essential that you fully explain what you are doing, why you are doing it and the steps involved in providing a final solution. Ensure your answer is not just a set of calculations as 25% of the marks for this question are set aside for your explanation.

Question 5-

A marketing consultant observed 50 consecutive shoppers at a supermarket. One variable of interest was how much each shopper spent in the store. The data are in Data of the Excel file called Assignment 2.xls (available from the portal).

(a) What sampling method was used? Was it the best choice of method for this data set?  Fully explain.

(b) Obtain a histogram of the data. Does it suggest a normal distribution for spending amounts?  Fully explain.

EXCEL Instructions: Add your ID to the column name for spending amounts. Please use the bins given in Data of Assignment 2.xls. Please make sure that the title of your histogram ends with your ID.

(c) Assume that the standard deviation is $22. Use EXCEL to calculate the sample mean (include a copy of the output in your submission). Then find and interpret a 95% confidence interval for the mean amount spent by shoppers in similar circumstances. Does the population have to be normal here? Fully explain.