Let x be a random variable that represents the pH of arterial plasma (i.e., acidity of the blood). For healthy adults, the mean of the x distribution is μ = 7.4†. A new drug for arthritis has been developed. However, it is thought that this drug may change blood pH. A random sample of 41 patients with arthritis took the drug for 3 months. Blood tests showed that x = 8.0 with sample standard deviation s = 1.8. Use a 5% level of significance to test the claim that the drug has changed (either way) the mean pH level of the blood. Solve the problem using the critical region method of testing (i.e., traditional method). (Round your answers to three decimal places.) test statistic = critical value = ± State your conclusion ion the context of the application. Reject the null hypothesis, there is sufficient evidence that the drug has changed the mean pH level.Reject the null hypothesis, there is insufficient evidence that the drug has changed the mean pH level. Fail to reject the null hypothesis, there is insufficient evidence that the drug has changed the mean pH level.Fail to reject the null hypothesis, there is sufficient evidence that the drug has changed the mean pH level. Compare your conclusion with the conclusion obtained by using the P-value method. Are they the same? We reject the null hypothesis using the traditional method, but fail to reject using the P-value method.The conclusions obtained by using both methods are the same. We reject the null hypothesis using the P-value method, but fail to reject using the traditional method.

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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The Student's t distribution table gives critical values for the Student's t distribution. Use an appropriate d.f. as the row header. For a right-tailed test, the column header is the value of α found in the one-tail area row. For a left-tailed test, the column header is the value of α found in the one-tail area row, but you must change the sign of the critical value t to −t. For a two-tailed test, the column header is the value of α from the two-tail area row. The critical values are the ±t values shown.

Let x be a random variable that represents the pH of arterial plasma (i.e., acidity of the blood). For healthy adults, the mean of the x distribution is μ = 7.4†. A new drug for arthritis has been developed. However, it is thought that this drug may change blood pH. A random sample of 41 patients with arthritis took the drug for 3 months. Blood tests showed that x = 8.0 with sample standard deviation s = 1.8. Use a 5% level of significance to test the claim that the drug has changed (either way) the mean pH level of the blood. Solve the problem using the critical region method of testing (i.e., traditional method). (Round your answers to three decimal places.)

test statistic	=
critical value	= ±

State your conclusion ion the context of the application.

Reject the null hypothesis, there is sufficient evidence that the drug has changed the mean pH level.Reject the null hypothesis, there is insufficient evidence that the drug has changed the mean pH level. Fail to reject the null hypothesis, there is insufficient evidence that the drug has changed the mean pH level.Fail to reject the null hypothesis, there is sufficient evidence that the drug has changed the mean pH level.

Compare your conclusion with the conclusion obtained by using the P-value method. Are they the same?

We reject the null hypothesis using the traditional method, but fail to reject using the P-value method.The conclusions obtained by using both methods are the same. We reject the null hypothesis using the P-value method, but fail to reject using the traditional method.

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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