Available below are amounts of arsenic in samples of brown rice from three different regions. The amounts are in micrograms of arsenic and all samples have the same serving size. Use a 0.05 significance level to test the claim that the three samples are from populations with the same mean. Do the amounts of arsenic appear to be different in the different regions? Given that the amounts of arsenic in the samples from region B have the highest mean, can we conclude that brown rice from region B poses the greatest health problem? Arsenic amounts (micrograms) A 1.8 3.6 4.1 4.2 4.5 4.5 4.6 4.9 5.1 5.2 5.3 5.8 B 5.6 5.7 6.7 6.9 6.9 6.9 7.1 7.2 7.4 7.5 7.7 7.8 C 4.6 4.7 5.2 5.5 5.6 5.6 5.6 5.7 6.1 6.1 6.2 6.4 What are the hypotheses to test? H0: H1: The test statistic is (Round to two decimal places as needed. The P-value is enter your response here. (Round to three decimal places as needed.) Since the P-value is ▼ greater less than the significance level, ___H0. There_sufficient evidence to refute the claim that the three samples are from populations with the same mean. Does this support a conclusion that the brown rice from region B poses the greatest health problem?

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

18th Edition

ISBN:9780079039897

Author:Carter

Publisher:Carter

Chapter10: Statistics

Section10.3: Measures Of Spread

Problem 26PFA

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Question

Available below are amounts of arsenic in samples of brown rice from three different regions. The amounts are in micrograms of arsenic and all samples have the same serving size. Use a

0.05

significance level to test the claim that the three samples are from populations with the same mean. Do the amounts of arsenic appear to be different in the different regions? Given that the amounts of arsenic in the samples from region B have the highest mean, can we conclude that brown rice from region B poses the greatest health problem?

Arsenic amounts (micrograms)


A	1.8	3.6	4.1	4.2	4.5	4.5	4.6	4.9	5.1	5.2	5.3	5.8
B	5.6	5.7	6.7	6.9	6.9	6.9	7.1	7.2	7.4	7.5	7.7	7.8
C	4.6	4.7	5.2	5.5	5.6	5.6	5.6	5.7	6.1	6.1	6.2	6.4

What are the hypotheses to test?

H0:

H1:

The test statistic is

(Round to two decimal places as needed.

The P-value is

enter your response here.

(Round to three decimal places as needed.)

Since the P-value is

▼

greater

less

than the significance level,

_____________H0. There___________sufficient evidence to refute the claim that the three samples are from populations with the same mean.

Does this support a conclusion that the brown rice from region B
poses the greatest health problem?

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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