Statistics for IT Managers: Final exam

Answer all three questions. Read each question very carefully, several times. I have indicated the points allocated for the subsections of each question. If you would like to perform some calculations or draw figures with your favorite statistical software or Excel, please do so. What is important is that you present all your answers to this exam in a ONE document. So for example if you decide to use Stata to draw a Table, add that Stata output to your Word document that contains answers to the rest of the exam.

Question One

(20 pts) A phenomenon of interest: horticulture, an area concerned with the growing of plants. Our units of analysis are plants that are a particular type of bulb. A bulb is any plant that stores its complete life cycle in an underground storage structure. Tulips, daffodils and hyacinths are examples of flowering bulbs. An onion is is another example of a bulb. When say a tulip bulb is planted in the soil, it may or may not germinate and produce a tulip

A horticulturist is experimenting with an altered bulb for a large plant. From previous experience, she knows that the percentage of these bulbs that germinate is either 50% or 75%. To decide which germination rate is correct, she plans an experiment involving 15 of these altered bulbs and records the number of bulbs that germinate. We assume that the number of bulbs that germinate follows a binomial model. Suppose before conducting the experiment, she sets the null hypothesis as p = 0.50 and alternative hypothesis as p = 0.75 and decides she will reject the null hypothesis if 11 or more bulbs germinate. The probabilities of all the possible germination outcomes from the experiment are shown below.

Required

1. (6 pts) For x = 9 in the above Table, explain with detailed workings, how the values of 0.1527 and 0.0917 are obtained
2. (7 pts) Using the Table data, calculate the probability of rejecting the null hypothesis when in fact it is true
3. (7 pts) Using the Table data, calculate the probability of accepting the null hypothesis when in fact it is false

(Note: For parts #2 and #3 above make sure you EXPLAIN your calculations)

Question two

(45 pts) Another phenomenon of interest, safety of elementary school children: A group of concerned parents wants speed bumps installed in front of a local elementary school, but the city traffic office is reluctant to allocate funds for this purpose. Both parties agree that bumps should be installed if the average speed of all motorists who pass the school while it is in session exceeds the posted speed limit of 15 miles per hour (mph).

So the parents and the city agreed to fund a study of traffic behavior on the street that runs by the school. As part of this study, over 3 days, a random sample of 150 motorists was observed and their speed measured. The sample mean was 15.3 mph and the sample standard deviation was 2.5 mph. Assume the observations are independent of each other.

Required

1. (5pts) State null and alternative hypotheses that are appropriate from the parents’ perspective. Clearly explain and defend the rationale for your choice
2. (5pts) State null and alternative hypotheses that are appropriate from the city traffic office’s perspective. Clearly explain and defend the rationale for your choice
3. (5pts) Adopting the parents’ perspective and assuming that they are willing to risk a 1% chance of committing a Type I error, what action should be taken?
4. (5pts) Adopting the city traffic office’s perspective and assuming that they are willing to risk a 10% chance of committing a Type I error, what action should betaken?
5. (5pts) Explain exactly what is meant by the phrase are willing to risk a 1% chance of committing a Type I error in the context of this problem
6. (5pts) Explain why parents are willing to risk a 1% chance of a Type I error while the city traffic office is comfortable with a risking a 10% chance on a Type I error
7. (5pts) Statisticians distinguish between statistical significance and material significance (practical importance in the context of the problem). To properly interpret the results of hypothesis testing, it is essential that one remember: Statistical significance is not the same as material significance. Using the calculations you performed, comment on the notions of statistical significance and material significance in the context of this problem
8. (5pts) Explain exactly what is meant by the phrase a random sample of 150 motorists was observed
9. (5pts) Give one reason why these 150 observations may not be really independent observations.

Question three

(35 pts) Let us study anew phenomenon of interest, burnout. Burnout is a state of emotional, mental, and physical exhaustion caused by excessive and prolonged stress. It occurs when you feel overwhelmed and unable to meet constant demands. As the stress continues, you begin to lose the interest or motivation that led you to take on a certain role in the first place. Burnout reduces your productivity and saps your energy, leaving you feeling increasingly helpless, hopeless, cynical, and resentful. Eventually, you may feel like you have nothing more to give. Burnout is a significant problem for people with careers in the field of human services such as those who work in hospitals or even for those who take part in competitive sports.

One of the popular and rigorously validated tools used to measure burnout is a scale called Maslach Burnout Inventory (MBI). This is a 22-item inventory (a kind of a survey) designed to measure three aspects of burnout:

Emotional exhaustion : measures feelings of being emotionally overextended and exhausted by one’s work

Depersonalization : measures an unfeeling and impersonal response toward recipients of one’s service, care treatment, or instruction

Personal accomplishment : measures feelings of competence and successful achievement in one’s work

The MBI tool is used extensively to assess professional burnout in the fields of human service, education, business, and government professions.

A study about burnout was done on 25 professionals who work in a large public hospital. The MBI was used to measure burnout for each person on a scale of 0 (no exhaustion) -1000 to create what is called the Exhaustion Index. Another variable called Concentration was also measured. Concentration is the proportion of social contacts with individuals who belong to a person’s work group. The data that was collected is shown below

The Minitab output for (1) scatter plot for the data and (2) the regression model is shown below. For convenience I’ve numbered the sections of the regression output as Section 1, ..., Section 5.

Required

1. (5 pts) One use of a regression model is for the purposes of prediction. I would like to use this model to predict Exhaustion Index for a Concentration value of 99%. Explain in detail why this would be or would not be appropriate given the information in this Minitab output
2. (5 pts) Is the regression equation significant? Explain
3. (5 pts) Section 3: Explain the meaning of R–Sq value of 61.2%
4. (5 pts) Section 4: Explain how the number 23 under the DF column is calculated
5. (5 pts) Section 4: Explain in detail the meaning of P= 0.000
6. (5 pts) Identify evidence in this Minitab output that would suggest we look for additional variables to explain Exhaustion Index
7. (5 pts) Suggest two additional variables we may consider for use together with Concentration to explain Exhaustion Index

Price: $31.19

Solution: The downloadable solution consists of 12 pages, 1919 words and 5 charts.
Deliverable: Word Document