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) Begin 107 110 123 129 112 111 107 112 136 102 Calcium Group End 100 114 105 112 115 116 106 102 125 104 Decrease 7 -4 18 17 -3 -5 1 10 11 -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 a. (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. b. (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 pvalue and the conclusion of the test. c. (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. d. (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. e. (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) 0-34 35-54 55-64 65+ Total NC population NC deaths 3,984,283 3,740 2,372,270 8,094 723,712 8,035 969,048 51,863 8,049,313 71,732 NC Agespecific rate (per 10,000) US population 139,328,990 82,826,479 24,274,684 34,991,753 281,421,906 US expected deaths per age group a. (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 tableyou can just report the numbers. b. (5) What is the crude death rate for North Carolina in 2000 (report as per 10,000)? c. (5) What is the age-adjusted death rate for North Carolina in 2000