A random sample is selected from a normal population with a mean of μ = 50 and a standard deviation of σ = 12. After a treatment is administered to the individuals in the sample, the sample mean is found to be M = 55. If the sample consists of n = 16 scores, is the sample mean sufficient to conclude that the treatment has a significant effect? Use a two tailed test with a α = .05. If the sample consists of n = 36 scores, is the sample mean sufficient to conclude that the treatment has a significant effect? Use a two tailed test with a α = .05. Comparing your answers for parts a and b, explain how the size of the sample influences the outcome of a hypothesis test.

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Description: A random sample is selected from a normal population with a mean of μ = 50 and a standard deviation of σ = 12. After a treatment is administered to the individuals in the sample, the sample mean is found to be M = 55. If the sample consists of n = 16

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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

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A random sample is selected from a normal population with a mean of μ = 50 and a standard deviation of σ = 12. After a treatment is administered to the individuals in the sample, the sample mean is found to be M = 55.

If the sample consists of n = 16 scores, is the sample mean sufficient to conclude that the treatment has a significant effect? Use a two tailed test with a α = .05.
If the sample consists of n = 36 scores, is the sample mean sufficient to conclude that the treatment has a significant effect? Use a two tailed test with a α = .05.
Comparing your answers for parts a and b, explain how 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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Step 1

Given information:

Population mean, $μ = 50$

Population standard deviation, $σ = 12$

The sample mean, M = 55

The level of significance, $α = 0.05$

It is required to:

1. determine whether the sample mean is sufficient to conclude that the treatment has a significant effect for a sample of size n = 16 scores.

2. determine whether the sample mean is sufficient to conclude that the treatment has a significant effect for a sample of size n = 36 scores.

3. compare the results of parts 1 and 2 that how the size of the sample is influencing the outcome of a hypothesis test.

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