A research article reported that for a random sample of 850 meal purchases made at fast food chain A, the mean sodium content was 1,681 mg, and the standard deviation was 822 mg. For a random sample of 2,107 meal purchases made at fast food chain B, the mean sodium content was 1,474 mg, and the standard deviation was 817 mg. Based on these data, is it reasonable to conclude that there is a difference in mean sodium content for meal purchases at fast food chain A and meal purchases at fast food chain B? Use ? = 0.05. (Use ?1 for fast food chain A and ?2 for fast food chain B.)State the appropriate null and alternative hypotheses.Find the test statistic and P-value. (Use SALT. Round your test statistic to one decimal place and your P-value to three decimal places.)t=P-value= State the conclusion in the problem context. We fail to reject H0. It is not reasonable to conclude that there is a difference in mean sodium content for meal purchases at fast food chain A and meal purchases at fast food chain B. We reject H0. It is not reasonable to conclude that there is a difference in mean sodium content for meal purchases at fast food chain A and meal purchases at fast food chain B. We reject H0. It is reasonable to conclude that there is a difference in mean sodium content for meal purchases at fast food chain A and meal purchases at fast food chain B. We fail to reject H0. It is reasonable to conclude that there is a difference in mean sodium content for meal purchases at fast food chain A and meal purchases at fast food chain B.

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Description: A research article reported that for a random sample of 850 meal purchases made at fast food chain A, the mean sodium content was 1,681 mg, and the standard deviation was 822 mg. For a random sample of 2,107 meal purchases made at fast food chain B,

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Calculus For The Life Sciences

2nd Edition

ISBN:9780321964038

Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Chapter13: Probability And Calculus

Section13.2: Expected Value And Variance Of Continuous Random Variables

Problem 10E

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A research article reported that for a random sample of 850 meal purchases made at fast food chain A, the mean sodium content was 1,681 mg, and the standard deviation was 822 mg. For a random sample of 2,107 meal purchases made at fast food chain B, the mean sodium content was 1,474 mg, and the standard deviation was 817 mg. Based on these data, is it reasonable to conclude that there is a difference in mean sodium content for meal purchases at fast food chain A and meal purchases at fast food chain B? Use ? = 0.05. (Use ?₁ for fast food chain A and ?₂ for fast food chain B.)

State the appropriate null and alternative hypotheses.

Find the test statistic and P-value. (Use SALT. Round your test statistic to one decimal place and your P-value to three decimal places.)

P-value=

State the conclusion in the problem context.

We fail to reject H₀. It is not reasonable to conclude that there is a difference in mean sodium content for meal purchases at fast food chain A and meal purchases at fast food chain B.

We reject H₀. It is not reasonable to conclude that there is a difference in mean sodium content for meal purchases at fast food chain A and meal purchases at fast food chain B.

We reject H₀. It is reasonable to conclude that there is a difference in mean sodium content for meal purchases at fast food chain A and meal purchases at fast food chain B.

We fail to reject H₀. It is reasonable to conclude that there is a difference in mean sodium content for meal purchases at fast food chain A and meal purchases at fast food chain B.

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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