A television documentary on overeating claimed that Americans are about 10 pounds overweight on average (μ). To test this claim, 18 randomly selected individuals were examined; their average (x̄) excess weight was found to be 12.4 pounds, and the sample standard deviation (s) was 2.7 pounds.

MNS601 – HOMEWORK ASSIGNMENT #3

Name: ___________________

Directions:  (a) Enter all your answers into this Word document in the space immediately following each question and submit the entire document.  .  (b) SHOW ALL YOUR WORK/calculations or results from a template.  When you use a template to calculate an answer, copy and paste the results into this document.  (c) While putting your answers in a different color font is helpful, please DO NOT use red font since this is the color used to provide feedback on your answers. 

  1. A television documentary on overeating claimed that Americans are about 10 pounds overweight on average (μ).  To test this claim, 18 randomly selected individuals were examined; their average (x̄) excess weight was found to be 12.4 pounds, and the sample standard deviation (s) was 2.7 pounds.  At a significance level of 0.01, is there any reason to doubt the validity of the claimed 10-pound value?  [15 POINTS]

ANSWER:

  • A stockbroker at Critical Securities reported that the mean rate of return on a sample of 10 oil stocks was 12.6 percent with a sample standard deviation of 3.9 percent.  The mean rate of return on a sample of 8 utility stocks was 10.9 percent with a sample standard deviation of 3.5 percent.  At the .05 significance level, can we conclude that there is more variation in the oil stocks?  [15 POINTS]

ANSWER:

  • A study compared the effects of four 1-month point-of-purchase promotions on sales.  The unit sales for five stores using all four promotions in different months follow.

                        Free Sample             78        87        81        89        85

                        On-pack gift              94        91        87        90        88

                        Cents off                    73        78        69        83        76

                        Refund by mail         79        83        78        69        81

At the 0.01 level of significance, do the promotions produce different effects on sales?  [Note:  There are 4 groups to compare, i.e., the 4 marketing methods.]   [20 POINTS]

ANSWER:

  • William Hawkins, VP of personnel for International Motors, is working on the relationship between a worker’s salary and absentee rate.  Hawkins divided the salary range of International into twelve grades or levels (1 being the lowest grade, 12 the highest) and then randomly sampled a group of workers.  He determined the salary grade for each worker and the number of days that employee had missed over the last 3 years.  [15 POINTS]

Salary ranking                11        10        8          5          9          9          7          3

Absences                        18        17        29        36        11        26        28        35

Salary ranking                11        8          7          2          9          8          6          3

Absences                        14        20        32        39        16        26        31        40

Construct a scatter diagram for these data and indicate the type of relationship.

ANSWER:

  • A study by the Atlanta, Georgia, Department of Transportation on the effect of bus ticket prices on the number of passengers produced the following results:

Ticket price (cents)        

25        30        35        40        45        50        55        60

Passengers per 100 miles

800     780     780     660     640     600     620     620

  1. Plot these data.  [5 POINTS]

ANSWER:

  1. Develop the estimating equation that best describes these data.  [10 POINTS]

ANSWER:

  1. Predict the number of passengers per 100 miles if the ticket price were 70 cents.  [5 POINTS]

ANSWER:

  • A financial consultant is interested in the differences in capital structure within different firm sizes in a certain industry.  The consultant surveys a group of firms with assets of different amounts and divides the firms into three groups.  Each firm is classified according to whether its total debt is greater than stockholders’ equity or whether its total debt is less than stockholders’ equity.  The results of the survey are:

Firm Asset Size (in $ thousands)

                                    <500               500-2,000                  2,000 +                       Total

Debt < equity            7                      10                                8                                  25

Debt > equity             10                    18                                9                                  37

             Total              17                  28                          17                              62

Do the three firm sizes have the same capital structure?  Use the 0.10 significance level.  [15 POINTS]

ANSWER: