QMB3200: Business and Economic Statistics II Exam #1

QMB3200: Business and Economic Statistics II Exam #1

Max. Score: 100 points

Instructions:

1)     All the questions must be answered.

2)     Show all the steps in your approach as you arrive at the final solution. Submitting only the final answer is not sufficient to get full credit.

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Additional Suggestions/Instructions:

1)     No need for typing. You can do your work by hand on  paper.

2)     If you use a regular A-4/Letter Size (8.5”x11”) paper to do your Homework on one side, perhaps it will be easier for you to scan. LEAVE ONE-INCH MARGIN ALL AROUND  SO THAT NOTHING GOES MISSING WHILE SCANNING. Ensure that in the scanned document the content on all pages is laid out Left to Right and Top to Bottom (whether the page is in Portrait or Landscape mode or in a combination there  of).

3)     Remember to write down your name on the report and number the  pages.

4)     Create a single scanned file. DO NOT SUBMIT MULTIPLE FILES. Verify and ensure everything with your report is in order so that when opened the layout is top to bottom. Word or pdf formats are acceptable. If you are using Excel ensure page setup is properly taken care of.

5)     Name your report file contains in its name, "Your Full Name" and "Exam  1".

6)     Upload your report file on Canvas and verify if everything is fine by opening up the uploaded file. It is your responsibility to ensure your report is uploaded  properly.

7)     Do not wait until the last minute. The deadline is strictly enforced by Canvas. No hardcopy submissions are accepted. No e-mail submissions are accepted. If the report does not appear in Canvas by the deadline, zero points will be recorded for you for Exam 1. No exceptions are entertained for any reason under any circumstance in this  regard.

8)    If anyone needs help with scanning, please stop by the Information Commons Help  Desk by the second floor Rotunda and seek help. They will explain what you need to do and you will be able to scan your work. Their service is totally free of charge for you. Information Commons is open 9 a.m. – 9 p.m. Monday through Thursday; 9 a.m. – 5 p.m. on Friday; and 8 a.m. – 5 p.m. on Saturday.

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1.      [20 points] Cars arrive at a car wash randomly and independently; the probability of an arrival is the same for any two time intervals of equal length. The mean arrival rate is 15 cars per hour.

a)      What is the probability that 12 or more cars will arrive during any given hour of operation? [5 points]

b)     What is the probability that 5 or fewer cars will arrive during any given 20 min. of operation?         [6 points]

c)      What is the probability that more than 5 but less than 10 cars will arrive during any given 40 min. of operation?                                                                                                            [6 points]

d)     What is the probability that no arrivals happen in any 10 min.  of operation?      [3 points]

2.      [20 points] Young children in the United States are exposed to an average of 4.0 hours of background television per day. Having the television on in the background while children are doing other activities may have adverse consequences on a child’s well-being. You have a research hypothesis that children from low-income families are exposed to more than 4.0  hours of daily background television. In order to test this hypothesis, you have collected a random sample of 60 children from low-income families and found that these children were exposed to a sample mean of 4.5 hours of daily background television. Based on a previous study, you are willing to assume that the population standard deviation is 1.0 hours. Use .01  as the level of significance.

a)      Develop hypotheses that can be used to test your  research hypothesis.               [3 points]

b)     What is the p-value based on your sample of 60 children from low-income families?   What is your hypothesis test decision based on p-value approach?                                          [6 points]

c)      Repeat the test using the critical value approach. What is your hypothesis test  decision?

[6 points]

d)     Are the results in b and c different? Why or why not?                                        [3 point]

e)      State your conclusion for the study.                                                                     [2 points]

3.      [20 points] A Poll showed that 25% of Americans are satisfied with the way things are going in the United States. Suppose a sample of 15 Americans is selected as part of a study of the state of the nation.

a)      Compute the probability that exactly 5 of the 15 Americans surveyed are satisfied with  the way things are going in the United States.                                                                                    [3 points]

b)     Compute the probability that at least 3 of the Americans surveyed are satisfied with the way things are going in the United States.                                                                                             [5 points]

c)      Compute the probability that no more than 4 of the Americans surveyed are satisfied with the way things are going in the United States.                                                                                    [4 points]

d)     Compute the probability that more than 2 but less than 6 of the Americans surveyed are satisfied with the way things are going in the United States.                                                            [5 points]

e)      Compute the expected value, variance, and standard deviation of the number of  Americans who are satisfied with the way things are going in the United States. [3  points]

4.      [20 points] A random sample of 50 passengers between the two airports flying by XYZ Airlines yielded a mean fare of $165. The population standard deviation of the fare is known to be $50.

a)      Develop a 94% confidence interval estimate on the fare between the two airports for  XYZ.            [6 points]

b)     Develop a 98% confidence interval estimate on the fare between the two airports for  XYZ.            [6 points]

c)      Develop the Hypothesis to answer the question “Is the mean fare between the two   airports on XYZ Airlines is different than $145?                                                                                         [3 points]

d)     Conduct the hypothesis test using the confidence Interval from part (b). What is your decision on the hypothesis stated in part c) above.                                                                       [3 points]

e)      What is your conclusion based on the decision from d)?                                     [2 points]

5.      [20 points] According to a Salary Survey Study, the average base salary for a brand manager in Houston, Texas, is $89,692 and the average base salary for a brand manager in Los Angeles, California, is $99,617. Assume that salaries are normally distributed, the standard deviation for brand managers in Houston is $19,800, and the standard deviation for brand managers in Los Angeles is $21,900.

a)      What is the probability that a brand manager in Houston has a base salary in excess  of

$110,000?                                                                                                            [5 points]

b)     What is the probability that a brand manager in Los Angeles has a base salary in excess   of $105,000?      [5 points]

c)      What is the probability that a brand manager in Houston has a base salary of less  than

$80,000?                                                                                                              [5 points]

d)     How much would a brand manager in Los Angeles have to make in order to have a   higher salary than 96% of the brand managers in Houston?                                                                     [5 points]