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CHI SQUARE HOMEWORK An occupancy rate is the proportion of a building’s rentable space that is occupied

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CHI SQUARE HOMEWORK

1. An occupancy rate is the proportion of a building’s rentable space that is occupied. It can be expressed as a ratio of occupied units divided by the total number of units. Suppose you would like to test the hypothesis that apartment project occupancy differs depending on proximity to public transportation. You randomly sample several small apartment buildings within walking distance to METRO and find a total of 250 units, with 240 being occupied (sample 1). You also randomly sample several small apartment buildings that are too far from mass transit to be considered within walking distance (sample 2). The second sample consists of 200 units, with 180 being occupied.

 

The null hypothesis is

H₀: occupancy rate is not associated (is independent of) with proximity to public transportation

 

and the alternative research hypothesis is

H_A: occupancy rate is associated (is dependent upon) proximity to public transportation.

 

1. Draw a 2x2 table demonstrating your data regarding proximity to METRO and occupancy rate.
2. Calculate the chi-square (χ ²)
3. Can you reject the null hypothesis?
4. Assuming a developer was interested in your findings, what recommendations would you make regarding where to buy property?

 

2. The state of Maryland has put a lot of effort into encouraging early voting.  A random sample of Maryland voters yielded 60 respondents aged 18-20 (sample 1), 42 of whom had voted early. Additionally, the sample included 40 respondents in the 21+ age category (sample 2), 15 of whom had voted early. Defining a “success” as having voted early, we can divide each sample into “success” and “failure” sub-categories: you will do a Chi-Square test following the steps below. Is early voting dependent upon age?
   1. State the null and alternative hypotheses for this test
   2. Create a 2 x 2 table displaying the data.
   3. Derive Chi-Square.
   4.  Determine, using the Chi-Square table, whether or not you should reject the null hypothesis.
   5. What might you conclude about age and early voting based on your results?

 

3. We have a campaign with three candidates: Candidate Adams, Candidate Butterfield, and Candidate Clayton, and Undecided. We find that 45 people support Adams, 48 support Butterfield, 44 support Clayton, and 15 were Undecided. Using the chi-square test, determine whether the voting pattern significantly differs from chance.
   1. At the .01 level of significance, report whether the Null and Research Hypotheses should be rejected or not.
   2. In your own words explain what these results indicate.

 

 

 

 

 

4. A job information survey was given to attendants in a mental hospital.  The survey included the question, "Are you satisfied in your present job?"   It was used to create two groups - a “Satisfied” group and an “Unsatisfied” group. These two groups represent two populations of employees - a population of unsatisfied employees and a population of satisfied employees .  After the survey was administered, the employment records of the attendants were examine and those who had voluntarily quit were noted.    The results for 30 attendants are as follows:  (S=Satisfied; U=Unsatisfied; W=Still working; Q=Quit): 

 

Person     Satisfaction               Whether                                                        Person                  Satisfaction               Whether

                  Group                         Quit                                                                                  Group                                    Quit

1             S                          W                                                     16          U                             Q

2            S                          Q                                                      17          U                             W

3            S                          W                                                     18          S                             W

4            S                          W                                                     19          U                             W

5            S                          W                                                     20         U                             Q

6            S                          Q                                                      21          U                             Q

7            U                         Q                                                      22          U                             Q

8            U                         Q                                                      23          U                             Q

9            U                         Q                                                      24          S                             W

10          U                         Q                                                      25          S                             W

11           U                         W                                                     26          U                             Q

12          S                          Q                                                      27          U                             W

13          S                          Q                                                      28         U                             W

14          S                          W                                                     29          S                             W

15          S                          Q                                                      30         S                             W

 

a.  What determines whether you’ll use a chi-square test?

 

b. What is the significance level recommended for chi-square tests?

 

c. Is there any relationship between job satisfaction and a person’s decision to quit this job?