A clinical trial is planned to compare an experimen- tal medication designed to lower blood pressure to a placebo. Before starting the trial, a pilot study is con- ducted involving seven participants. The objective of the study is to assess how systolic blood pressure changes over time untreated. Systolic blood pressures are measured at baseline and again 4 weeks later. Is there a statistically significant difference in blood pressures over time? Run the test at a 5% level of sig- nificance. Baseline 120 145 130 160 152 143 126 4 weeks 122 142 135 158 155 140 130
Equations and Inequations
Equations and inequalities describe the relationship between two mathematical expressions.
Linear Functions
A linear function can just be a constant, or it can be the constant multiplied with the variable like x or y. If the variables are of the form, x2, x1/2 or y2 it is not linear. The exponent over the variables should always be 1.
Introduction:
Denote μ1, μ2 as the true mean systolic blood pressure at baseline, and 4 weeks later, respectively.
Denote, μd = μ1 – μ2 as the mean of the differences in the blood pressure values at the two periods.
Since it is of interest to know whether there is a significant difference in blood pressure values over time, the null and alternative hypotheses are as follows:
H0: μd = 0, versus H1: μd ≠ 0.
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