Answered: A random sample of 25 women resulted in…

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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A random sample of 25 women resulted in systolic blood pressure levels with a mean of 142 and a standard deviation of 6.9. A random sample of 61 men resulted in systolic blood pressure levels with a mean of 92 and a standard deviation of 2. Use a 0.025 significance level and the p-value method to test the claim that blood pressure levels for women vary more than blood pressure levels for men.

Enter the smallest critical value. (Round your answer to nearest ten-thousandth.)

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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Step 1

Given:

The sample size of the women resulted in systolic blood pressure levels is $n_{1} = 25$ .

The sample size of the men resulted in systolic blood pressure levels is $n_{2} = 61$ .

The sample mean of the women resulted in systolic blood pressure levels is ${\bar{x}}_{1} = 142$ .

The sample mean of the men resulted in systolic blood pressure levels ${\bar{x}}_{2} = 92$ .

The sample standard deviation of the women resulted in systolic blood pressure levels $s_{1} = 6.9$ .

The sample standard deviation of the men resulted in systolic blood pressure levels $s_{2} = 2$ .

The level of significance is $α = 0.025$ .

The researcher claims that the blood pressure levels for women vary more than blood pressure levels for men. So the statistical hypothesis formed is:

H0: $μ_{1} \leq μ_{2}$

H1: $μ_{1} > μ_{2}$

where $μ_{1} a n d μ_{2}$ are the true representative of the population mean of blood pressure levels for women and men.

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