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# P-Values, Null Hypotheses and Confidence Intervals

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I have some trouble understanding the concept first and it will be really helpful if I can see the problem worked out. Here is example question from the textbook. Please help me.

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 is seated systolic blood pressure at the beginning and end of the 12 weeks measured in mm Hg. The data includes the decrease after 12 weeks (a negative value indicates an increase.

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
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

A. Look at the calcium data as paired. 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. Show the steps you used to reach the conclusions.

Which equation should be used?

B. Treat the two groups as independent samples, equal variances. Look only at the decrease columns. 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.

C. Treat the two groups as independent samples, unequal variances. Look only at the decrease columns. 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. Compare the results from all three tests. Try to explain any discrepancies, if any exist.