A clinical trial is run to assess the effectiveness of a new drug in lowering blood pressure. Patients are randomized to receive the new drug or placebo and systolic blood pressure is measured after 12 weeks on the assigned treatment. Is the mean systolic blood pressure for patients in the new drug group significantly lower than the mean systolic blood pressure for patients in the placebo group after the 12 week treatment?
Transcribed Image Text:Sample Size
Mean
Std Dev
New Drugi
Placebo₂
15
118.2
14.3
15
122.6
15.1
Definition Definition Measure of central tendency that is the average of a given data set. The mean value is evaluated as the quotient of the sum of all observations by the sample size. The mean, in contrast to a median, is affected by extreme values. Very large or very small values can distract the mean from the center of the data. Arithmetic mean: The most common type of mean is the arithmetic mean. It is evaluated using the formula: μ = 1 N ∑ i = 1 N x i Other types of means are the geometric mean, logarithmic mean, and harmonic mean. Geometric mean: The nth root of the product of n observations from a data set is defined as the geometric mean of the set: G = x 1 x 2 ... x n n Logarithmic mean: The difference of the natural logarithms of the two numbers, divided by the difference between the numbers is the logarithmic mean of the two numbers. The logarithmic mean is used particularly in heat transfer and mass transfer. ln x 2 − ln x 1 x 2 − x 1 Harmonic mean: The inverse of the arithmetic mean of the inverses of all the numbers in a data set is the harmonic mean of the data. 1 1 x 1 + 1 x 2 + ...
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