1. Use the following data set to perform the t-test and determine p-values:
The data studies the effect of dietary calcium on blood pressure. In the experiment, one group of black male adults received calcium supplements for 12 weeks. A control group of black male adults was given placebos for 12 weeks. Earlier tests indicated that calcium could be more effective in the black population. The data are seated systolic blood pressure at the beginning and end of the 12 weeks measured in mm Hg. The data include the decrease after 12 weeks (a negative value indicates an increase).
If you choose to use the table for calculating the p value range, please also report what you calculated for t (or for F)!!!!!! Data from Lyle et al., JAMA 257:1772-1776 (1987)
Calcium Group
Begin End Decrease
107 100 7
110 114 -4
123 105 18
129 112 17
112 115 -3
111 116 -5
107 106 1
112 102 10
136 125 11
102 104 -2
Placebo Group
Begin End Decrease
123 124 -1
109 97 12
112 113 -1
102 105 -3
98 95 3
114 119 -5
119 114 5
112 114 -2
110 121 -11
117 118 -1
130 133 -3
- (4) Look at the calcium data as paired. Perform a test to determine the p-value (two-sided) for the decrease. State the null and alternative hypothesis. Calculate a 95% confidence interval for the decrease. Show the steps you used to reach the conclusions. If you use statistical software, show which equations must be used.
- (4) Perform the F test to compare variances on the decrease columns. You will be comparing the variance of the decrease column for calcium to the decrease column for placebo. State the p-value and the conclusion of the test.
- (4) Treat the two groups (calcium and placebo) as independent samples, equal variances. Look only at the decrease columns (you are now comparing the calcium decrease column to the placebo decrease column). Perform a test to determine the p-value for the decrease. State the null and alternative hypothesis. Calculate a 95% confidence interval for the decrease.
- (4) Treat the two groups as independent samples, unequal variances. Look only at the decrease columns (calcium vs. placebo). Perform a test to determine the p-value for the decrease. State the null and alternative hypothesis. Calculate a 95% confidence interval for the decrease.
- (4) Do a two-sided t-test to compare the sample groups. Look at the Begin column for calcium and the Begin column for placebo. Report the p-value. Based on that p-value, do you have any reason to believe that the sample groups were significantly different headed into the experiment?
2. Use the direct method of standardization to compute the crude mortality rate and age-adjusted mortality rate for North Carolina in 2000. Use the U.S. population (also in table) as your standardizing population.
|
Age (years)
|
NC population
|
NC deaths
|
NC Age-specific rate (per 10,000)
|
US population
|
US expected deaths per age group
|
|
0-34
|
3,984,283
|
3,740
|
|
139,328,990
|
|
|
35-54
|
2,372,270
|
8,094
|
|
82,826,479
|
|
|
55-64
|
723,712
|
8,035
|
|
24,274,684
|
|
|
65+
|
969,048
|
51,863
|
|
34,991,753
|
|
|
Total
|
8,049,313
|
71,732
|
|
281,421,906
|
|
(5) Fill in the missing values for the age-specific rates in North Carolina, and the expected deaths in the U.S. population using the North Carolina rates. You do not have to list in the table-you can just report the numbers.
- (5) What is the crude death rate for North Carolina in 2000 (report as per 10,000)?
- (5) What is the age-adjusted death rate for North Carolina in 2000?