Problem 1: It has been hypothesised that the probability of having an asthma attack on a particular day may vary across the days of the week. Baibergenov et al. (2005) report a longitudinal study in which the number of emergency department admissions due to asthma were recorded in Ontario between April 2001 and March 2004. Suppose the data were as in the table below:
|
Day of attack
|
Mon
|
Tues
|
Wed
|
Thur
|
Fri
|
Sat
|
Sun
|
|
Number recorded
|
15555
|
13772
|
13548
|
12782
|
12416
|
13943
|
16820
|
Baibergenova, A., Thabane, L., Akhtar-Danesh, N., Levine, M., Gafni, A., Moineddin, R. and Pulcins, I. (2005): Effect of gender, age, and severity of asthma attack on patterns of emergency department visits due to asthma by month and day of the week. European Journal of Epidemiology20, No.11, 947-956.
Part a) Which graphical method would best display the above data?
A. A stem-and-leaf plot
B. A bar chart
C. A histogram
D. A pie chart
E. A boxplot
Part b) Which of the following best describes the null hypothesis?
A. The probability of having an asthma attack in Ontario on a particular day does not vary across the days of the week.
B. The probability of having an asthma attack in Ontario on a particular day varies across the days of the week.
C. The mean number of asthma attacks in Ontario per day varies by day of the week.
D. The number of asthma attacks in Ontario per day varies by day of the week.
E. There is no variation in the daily number of asthma attacks in Ontario.
Part c) Under the null hypothesis, what would be the expected number of emergency admissions due to asthma in Ontario on a Tuesday?
Give your answer to 2 decimal places.
Part d) Compute your test statistic here using R, giving your answer to 2 decimal places.
Part e) Provide the P-value of your test to 3 decimal places.
Problem 2
Section Shown
(1 pt) So-called racial steering occurs when a real estate agent has a tendency to show prospective property buyers only homes in neighbourhoods already dominated by the race of the prospective buyer. Such action violates the Fair Housing Act of 1968 in the USA. Connor and Kadane (2001) write about an American court case where it was alleged that a real estate agent was applying racial steering to renters. Data were provided about how the race of a potential renter of an apartment in a complex appeared to influence the section in the complex the realtor showed the potential renter. The complex split into two sections, section A which was predominantly white and B which was predominantly black. Suppose the data over a two-year period were as below:
|
Potential Renter Race
|
|
|
White
|
Black
|
|
A
|
70
|
25
|
|
B
|
79
|
38
|
Connor, J.T. and Kadane, J.B. (2001): Alleged racial steering in an apartment complex. Chance 14, No.2, 19-22.
Part a) What hypothesis (or hypotheses) are of interest to test in this context? (Choose all that apply.)
A. There is no dependence between the race of a potential renter and the section they are shown by the realtor in the complex.
B. White potential renters are just as likely to rent an apartment in the complex as black potential renters.
C. There was no difference between the number of white and black potential renters.
D. The chance of being shown an apartment in each section does not depend on the race of the potential renter.
E. There was no difference in the numbers of apartments being available to rent in the two sections of the complex.
Part b) Select a hypothesis you chose above. A test that can be applied here takes as its test statistic the count, Z say, in the top left hand cell in the table, assuming that the marginal totals in the table are fixed.
Under the null hypothesis, find the probability of the value of Z observed in the table, to three decimal places.
Part c) If using this hypothesis test in this context would you adopt a one-sided or two-sided alternative hypothesis?
A. One-sided
B. Two-sided
C. It does not matter
Part d) Perform your test using R. Find the P-value for the test, to three decimal places.
Part e) Would you reject or not reject your null hypothesis at the 5% significance level?
A. Reject
B. Not reject