Lower blood pressure: Five individuals with high blood pressure were given a new drug that was designed to lower blood pressure (in mmHg) was measured before and after treatment for each individual, with the following results: Before<-c(170, 164, 168, 158, 183)After<-c(145, 132, 129, 135, 145) Construct a 98% confidence interval for the mean reduction in systolic blood pressure. Hint: Using R, and examples in Lecture Notes Paired t-testdata: Before and Aftert = 9.6173, df = 4, p-value = 0.0006535alternative hypothesis: true difference in means is not equal to 099 percent confidence interval: 16.36779 46.43221sample estimates:mean of the differences 31.4 ------------------------------------------------------------ Paired t-testdata: Before and Aftert = 9.6173, df = 4, p-value = 0.0003268alternative hypothesis: true mean difference is greater than 098 percent confidence interval: 21.60991 Infsample estimates:mean difference 31.4 ------------------------------------------------------------- Paired t-testdata: Before and Aftert = 9.6173, df = 4, p-value = 0.0006535alternative hypothesis: true difference in means is not equal to 098 percent confidence interval: 19.16635 43.63365sample estimates:mean of the differences 31.4 -------------------------------------------------------------------- Welch Two Sample t-testdata: Before and Aftert = 5.913, df = 7.6402, p-value = 0.0004252alternative hypothesis: true difference in means is not equal to 098 percent confidence interval: 15.84445 46.95555sample estimates:mean of x mean of y 168.6 137.2 a.( 16.36779, 46.43221) b. (24.43959, 38.36041) c.(21.61, Inf) d.(15.84445, 46.95555)

Before<-c(170, 164, 168, 158, 183)After<-c(145, 132, 129, 135, 145)

Answered: Lower blood pressure: Five individuals…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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Question

Lower blood pressure: Five individuals with high blood pressure were given a new drug that was designed to lower blood pressure (in mmHg) was measured before and after treatment for each individual, with the following results:

Before<-c(170, 164, 168, 158, 183)

After<-c(145, 132, 129, 135, 145)

Construct a 98% confidence interval for the mean reduction in systolic blood pressure.

Hint: Using R, and examples in Lecture Notes

Paired t-test

data: Before and After
t = 9.6173, df = 4, p-value = 0.0006535
alternative hypothesis: true difference in means is not equal to 0
99 percent confidence interval:
16.36779 46.43221
sample estimates:
mean of the differences
31.4

------------------------------------------------------------

Paired t-test

data: Before and After
t = 9.6173, df = 4, p-value = 0.0003268
alternative hypothesis: true mean difference is greater than 0
98 percent confidence interval:
21.60991 Inf
sample estimates:
mean difference
31.4

-------------------------------------------------------------

Paired t-test

data: Before and After
t = 9.6173, df = 4, p-value = 0.0006535
alternative hypothesis: true difference in means is not equal to 0
98 percent confidence interval:
19.16635 43.63365
sample estimates:
mean of the differences
31.4

--------------------------------------------------------------------

Welch Two Sample t-test

data: Before and After
t = 5.913, df = 7.6402, p-value = 0.0004252
alternative hypothesis: true difference in means is not equal to 0
98 percent confidence interval:
15.84445 46.95555
sample estimates:
mean of x mean of y
168.6 137.2

a.

( 16.36779, 46.43221)

b.

(24.43959, 38.36041)

c.

(21.61, Inf)

d.

(15.84445, 46.95555)

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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