For a hypothesis test of a single population mean with unknown population standard deviation (σ�), we can use either Geogebra or Minitab. In Geogebra: use the “Statistics” tab in the Probability Calculator. Click the drop-down menu near the top (default is “Z Test of a Mean”) and choose “T Test of a Mean.” In Minitab: Select Stat > Basic Statistics > 1 sample t. Select Summarized Data from the drop-down menu. Check mark “Perform Hypothesis Test” and enter the hypothesized value. Click Options and select the appropriate alternate hypothesis. For both: Enter the sample mean, sample standard deviation, and sample size. We’ll use a sample with x¯=73.2�¯=73.2, s=14.16�=14.16, n=16�=16. For a hypothesis test of H0:μ=70 versus HA:μ>70�0:�=70 versus ��:�>70: The given sample has a test statistic of equation editor Equation Editor . The P-value for the test is equation editor Equation Editor . For a hypothesis test of H0:μ=75 versus HA:μ<75�0:�=75 versus ��:�<75: The given sample has a test statistic of equation editor Equation Editor . The P-value for the test is equation editor Equation Editor . For a hypothesis test of H0:μ=75 versus HA:μ≠75�0:�=75 versus ��:�≠75: The given sample has a test statistic of equation editor Equation Editor . The P-value for the test is equation editor Equation Editor

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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Question

For a hypothesis test of a single population mean with unknown population standard deviation (σ�), we can use either Geogebra or Minitab.

In Geogebra: use the “Statistics” tab in the Probability Calculator. Click the drop-down menu near the top (default is “Z Test of a Mean”) and choose “T Test of a Mean.”

In Minitab: Select Stat > Basic Statistics > 1 sample t. Select Summarized Data from the drop-down menu. Check mark “Perform Hypothesis Test” and enter the hypothesized value. Click Options and select the appropriate alternate hypothesis.

For both: Enter the sample mean, sample standard deviation, and sample size. We’ll use a sample with x¯=73.2�¯=73.2, s=14.16�=14.16, n=16�=16.

For a hypothesis test of H0:μ=70 versus HA:μ>70�0:�=70 versus ��:�>70:

The given sample has a test statistic of

equation editor
Equation Editor
.
The P-value for the test is

equation editor
Equation Editor
.

For a hypothesis test of H0:μ=75 versus HA:μ<75�0:�=75 versus ��:�<75:

The given sample has a test statistic of

equation editor
Equation Editor
.
The P-value for the test is

equation editor
Equation Editor
.

For a hypothesis test of H0:μ=75 versus HA:μ≠75�0:�=75 versus ��:�≠75:

The given sample has a test statistic of

equation editor
Equation Editor
.
The P-value for the test is

equation editor
Equation Editor
.

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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