A random sample is selected from a normal populationwith a mean of μ = 50 and a standard deviation ofσ = 12. After a treatment is administered to theindividuals in the sample, the sample mean is foundto be M = 55.If the sample consists of n = 16 scores, is thesample mean sufficient to conclude that thetreatment has a significant effect? Use atwo-tailed test with α = .05.If the sample consists of n = 36 scores, is thesample mean sufficient to conclude that thetreatment has a significant effect? Use atwo-tailed test with α = .05.Comparing your answers for parts a and b, explainhow the size of the sample influences the outcomeof a hypothesis test.

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Description: A random sample is selected from a normal populationwith a mean of μ = 50 and a standard deviation ofσ = 12. After a treatment is administered to theindividuals in the sample, the sample mean is foundto be M = 55.If the sample consists of n = 16 scor

We know that the population mean and the standard deviation is given as: After the treatment is…

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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 random sample is selected from a normal populationwith a mean of μ = 50 and a standard deviation of

σ = 12. After a treatment is administered to theindividuals in the sample, the sample mean is found

to be M = 55.

If the sample consists of n = 16 scores, is thesample mean sufficient to conclude that the

treatment has a significant effect? Use atwo-tailed test with α = .05.

If the sample consists of n = 36 scores, is thesample mean sufficient to conclude that the

treatment has a significant effect? Use atwo-tailed test with α = .05.

Comparing your answers for parts a and b, explainhow the size of the sample influences the outcome

of a hypothesis test.

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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