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Name: A drug company developed a drug D that they believe will reduce choles
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Description: A drug company developed a drug D that they believe will reduce cholesterol in men. It is known that the mean cholesterol level of males between the ages of 20 and 74 years old living in the United States is μ = 211 mg (per 100 ml), with a standard d

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 drug company developed a drug D that they believe will reduce cholesterol in men. It is known that the mean cholesterol level of males between the ages of 20 and 74 years old living in the United States is μ = 211 mg (per 100 ml), with a standard deviation of σ = 46 mg (per 100 ml). To test this belief, the company recruited n=1000 males between the ages of 20 and 74 years old living in the United States and gave them drug D over the course of 3 months. At the end of the 3 month drug treatment, cholesterol level was tested for these n=1000 study participants. Their mean cholesterol level was found to be MD = 200 ml (per 100 ml). Perform a z-test by answering the questions below. Use an alpha-level of α=.05.

1. What is the research hypothesis, H1?

2. What is the null hypothesis, H0?

3. What is the critical value of z, z_crit? (Be sure to use a + or a - sign for your answer.)

4. What is the mean of the distribution of sample means, μ_M?

5. What is the standard deviation of the distribution of sample means, σ_M?

6. What is the z-score of the sample mean, M_D?

7. Based on the relation between the critical value of z and the z-score of the sample mean, can you reject the null hypothesis?

8. Based on whether or not you can reject the null hypothesis, can you accept the research hypothesis?

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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