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Name: A laboratory claims that the mean sodium level, µ, of a healthy adult
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Description: A laboratory claims that the mean sodium level, µ, of a healthy adult is 138 mEq per liter of blood. To test claim, a random sample of 100 adult patients is evaluated. The mean sodium level for the sample is 137 mEq per liter of blood. It is known th

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 laboratory claims that the mean sodium level, µ, of a healthy adult is 138 mEq per liter of blood. To test claim, a random sample of 100 adult patients is evaluated. The mean sodium level for the sample is 137 mEq per liter of blood. It is known that the population standard deviation of adult sodium levels is 11 mEq. Can we conclude, at the 0.01 level of significance, that the population mean adult sodium level differs from that claimed by the laboratory?

Perform a two-tailed test. Then fill in the table below.

Carry your intermediate computations to at least three decimal places, and round your responses as specified in the table.

The null hypothesis: H₀ : _____

The alternative hypothesis: H₁: ______

The type of test statistic: (choose one) _______

The value of the test statistic: ______

(round to at least three decimal places.)

The p-value: _____

(round to at least three decimal places.)

Can we conclude that the population mean adult sodium level differs from that claimed by the laboratory? Yes _____, NO ______

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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Consider that μ is the population mean sodium level for a healthy adult.

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