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Name: A cardiologist wants to determine whether there is a change in blood p
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Description: A cardiologist wants to determine whether there is a change in blood pressure when her patients are given a new medication. She samples 45 patients and measures their systolic blood pressure. After ten weeks on the medication, the same 45 patients ha

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018

18th Edition

ISBN:9780079039897

Author:Carter

Publisher:Carter

Chapter4: Equations Of Linear Functions

Section4.5: Correlation And Causation

Problem 15PPS

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A cardiologist wants to determine whether there is a change in blood pressure when her patients are given a new medication. She samples 45 patients and measures their systolic blood pressure. After ten weeks on the medication, the same 45 patients have their blood pressure measured again. The cardiologist is interested in estimating the mean difference in systolic blood pressure levels after taking the new medication. The mean difference (after medication - before medication) for the 45 sampled patients is -2 mmHg and the sample standard deviation is 0.4 mmHg.

In one complete sentence, explain why the researcher will need to use paired t-methods when constructing the confidence interval for the mean difference in blood pressure.

When constructing a 95% confidence interval for the mean difference in systolic blood pressure after taking the medication, what value should be used for the point estimate?

Calculate the margin of error for the 95% confidence interval for the mean difference in blood pressure.

True or False: There is a 95% chance that the true mean difference in blood pressure after taking the new medication is between -2.210 mmHg and -1.880 mmHg.

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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