Below are two questions from my mid-term that I did not get right and am just very confused with HOW to get the answers. What equations am I using for each part? I'd like to know the why behind the equations to use so that I can do it in the future and I seem to be missing a key element. I found similar uploaded to this site but they just had the answers, not HOW to get them.

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).

Data from Lyle et al., JAMA 257:1772-1776 (1987)

Calcium Group

BeginEndDecrease

1071007

110114-4

12310518

12911217

112115-3

111116-5

1071061

11210210

13612511

102104-2

Placebo Group

BeginEndDecrease

123124-1

1099712

112113-1

102105-3

98953

114119-5

1191145

112114-2

110121-11

117118-1

130133-3

1. 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.
2. 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.
3. 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.
5. Utilize 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 following data table comparing a control group to a group with paclitaxel coated angioplasty balloons implanted in leg arteries:

Variables control group balloons group

(n = 54) (n = 48)

Baseline Rutherford stage 3.1 0.8 3.4 0.8

Degree of stenosis 91 7 89 8

Target lesion length (cm) 7.4 6.7 7.5 6.2

Target lesion diameter (cm) 4.7 0.6 5.0 0.7

No. of runoff vesicles 2.1 0.8 1.8 0.8

NOTE. Values are mean SD.

Data taken from Tepe et al. (2008) N Eng J Med. 358(7):689-699.

a.Perform the F test on all five variables listed (comparing control group to balloons group). State the p-value and conclusions that should include whether to use the equal variance approach or the unequal variance approach.

b.Perform hypothesis tests on all five variables (again comparing one group to the other). State the null hypothesis for each. List the p-value and a specific conclusion.

c.Calculate by hand the Satterthwaite's degrees of freedom for target lesion diameter (the fourth variable). Show your steps. Your answer should be the exact number that would be used in a table to look up the p-value in the subsequent hypothesis test.

d.Construct a 99% confidence interval for degree of stenosis, balloons group.