1. We want to test if more than 10% of patients receiving a certain type of medication experience nausea. We randomly sample 20 such patients, and note that 4 experience nausea.
a. At a = .05, use the exact Binomial approach to carry out the test. That is, "by hand", calculate the p-value and interpret the result.
b. Use PROC FREQ to obtain the p-value. Turn in the printout, and highlight the p-value.
2. Of 259 people with a kidney disease, 214 have a "positive" result on a screening test.
a. Give a point estimate and a (large-sample) 95% confidence interval for the proportion of all patients with this disease who would have such a result on this screening test.
b. Using the large-sample (Z-test) approach, test if the true proportion differs from .75. Using a = .05, perform the test "by hand", and interpret the result.
c. Use PROC FREQ to obtain the test statistic and p-value. Turn in the printout, and highlight the p-value.
3. Use the REACTIONTIME data set. First, use if-then statements to create a new variable which dichotomizes reaction time into 'fast' (< 400) or 'slow' (> 400). Then, sort the data set by both sex and this new variable. To do this, use PROC SORT, and in the BY statement write sex and the name of the new variable.
data three;
set reactiontime;
if reaction >= 400 then react2 = 'fast';
else react2 = 'slow';
run;
Next, use PROC FREQ, with the PDIFF option, to obtain a two-way table, where sex defines the rows and your new variable defines the columns. Do not turn in the printout, but answer the following questions.
a. Give a point estimate for the proportion with a 'fast' reaction time for each sex.
b. Give the 95% confidence interval for the difference in the proportions.
c. Using only the CI in (b), can we detect a difference in the proportions? Why or why not? Interpret the result as you would a two-sided hypothesis test.
d. Again use PROC FREQ, now with the CHISQ option, to obtain a two-way table. Do not turn in the printout, but report the test statistic and p-value of the test. Are the results here consistent with what you reported in part (c)? Why or why not?
4. Again use the REACTIONTIME data set. Now use PROC FREQ to obtain a two-way table of stimulus type with your new variable, and include the CHISQ option. Do not turn in the printout, but answer the following questions.
a. State the test statistic and p-value, and briefly interpret the result. Use a = .05.
b. State the proportion who are 'fast' for each stimulus type. Then, based on this, where do you think you would find "significant" differences if you were to compare each pair of stimulus types? Note that you are not expected to make any further calculations beyond the original 2x3 table - just use the proportions to aid in answering this.
5. Twenty-one patients who underwent shoulder surgery were later judged to have had complete or incomplete recovery. We also noted whether or not each patient went to physical therapy (PT) after surgery. Using the data in the table below, at a = .05, we want to see if patients who go to PT have a higher proportion of complete recovery than those who do not.
PT
Yes No
|
Complete
|
10
|
3
|
|
Incomplete
|
2
|
6
|
a. Calculate the c2 test statistic, "by hand", using the "shortcut" method. Show your work.
b. Use PROC FREQ to obtain the two-way table for this data, and include the CHISQ option. Turn in the printout.
c. Give at least one reason we should not use the c2 test in this situation.
6. One hundred and fifty restaurants in the greater Columbia area were rated by both the state health department (DHEC) and an independent company. Each gave a restaurant a rating of 'A' or 'other'. Both gave an 'A' to 108 restaurants; DHEC gave an 'A' while the independent company gave an 'other' to 13 restaurants; DHEC gave an 'other' while the independent company gave an 'A' to 2 restaurants; both gave an 'other' to 27 restaurants.
a. Display the data in an appropriate 2x2 table.
b. Test, at a = .05, if there is a difference in the proportion given an 'A' between DHEC and the independent company. Use the exact procedure, not the large-sample version.
c. Calculate an appropriate measure of agreement between DHEC and the independent company.