Answered: Suppose medical researchers think that…

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

Suppose medical researchers think that

p = 0.70

is the proportion of all teenagers with high blood pressure whose blood pressure would decrease if they took calcium supplements. To test this theory, the researchers plan a clinical trial (experiment) in which

n = 230

teenagers with high blood pressure will take regular calcium supplements.

(a)

Assume that

p = 0.70

actually is the population proportion that would experience a decrease in blood pressure. What are the numerical values of the mean and standard deviation of the sampling distribution of p̂, the sample proportion, for samples of

n = 230

teenagers? (Round your standard deviation to four decimal places.)

mean standard deviation

(b)

Use the results of part (a) and the Empirical Rule to calculate an interval that will contain the sample proportion p̂ for about 99.7% of all samples of

n = 230

teenagers. (Round your answers to three decimal places.)

between________ and___________

(c)

In the clinical trial, 120 of the 230 teenagers taking calcium supplements experienced a decrease in blood pressure. What is the value of p̂ for this sample?

p̂ =

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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