In a test of the effectiveness of garlic for lowering cholesterol, 49 subjects were treated with raw garlic. Cholesterol levels were measured before and after the treatment. The changes (before minus after) in their levels of LDL cholesterol (in mg/dL) have a mean of 0.8 and a standard deviation of 1.51. Use a 0.10 significance level to test the claim that with garlic treatment, the mean change in LDL cholesterol is greater than 0. What do the results suggest about the effectiveness of the garlic treatment? Assume that a simple random sample has been selected. Identify the null and alternative hypotheses, test statistic, P-value, and state the final conclusion that addresses the original claim. What are the null and alternative hypotheses? A. H0: μ=0 mg/dL H1: μ<0 mg/dL B. H0: μ>0 mg/dL H1: μ<0 mg/dL C. H0: μ=0 mg/dL H1: μ≠0 mg/dL D. H0: μ=0 mg/dL H1: μ>0 mg/dL 2) Determine the test statistic. (Round to two decimal places as needed.) Determine the P-value. (Round to three decimal places as needed.) 3) State the final conclusion that addresses the original claim. (OPTION 1-Reject, OPTION 2- Fail to reject) Ho. There is (OPTION 1-sufficient, OPTION 2-not sufficient) evidence to conclude that the mean of the population of changes (OPTION 1-equal to, OPTION 2-is greater than, OPTION 3-is not, OPTION 4-is less than) 0.

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018

18th Edition

ISBN:9780079039897

Author:Carter

Publisher:Carter

Chapter10: Statistics

Section: Chapter Questions

Problem 22SGR

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In a test of the effectiveness of garlic for lowering cholesterol, 49 subjects were treated with raw garlic. Cholesterol levels were measured before and after the treatment. The changes (before minus after) in their levels of LDL cholesterol (in mg/dL) have a mean of 0.8 and a standard deviation of 1.51. Use a 0.10 significance level to test the claim that with garlic treatment, the mean change in LDL cholesterol is greater than 0. What do the results suggest about the effectiveness of the garlic treatment? Assume that a simple random sample has been selected. Identify the null and alternative hypotheses, test statistic, P-value, and state the final conclusion that addresses the original claim.

What are the null and alternative hypotheses?

H0: μ=0 mg/dL

H1: μ<0 mg/dL

H0: μ>0 mg/dL

H1: μ<0 mg/dL

H0: μ=0 mg/dL

H1: μ≠0 mg/dL

H0: μ=0 mg/dL

H1: μ>0 mg/dL

Determine the test statistic.

(Round to two decimal places as needed.)

Determine the P-value.

(Round to three decimal places as needed.)

State the final conclusion that addresses the original claim.

(OPTION 1-Reject, OPTION 2- Fail to reject) Ho. There is (OPTION 1-sufficient, OPTION 2-not sufficient) evidence to conclude that the mean of the population of changes (OPTION 1-equal to, OPTION 2-is greater than, OPTION 3-is not, OPTION 4-is less than) 0.

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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