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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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Data Set:

Question 9: Create a confidence interval for the mean. Use 90, 95, or 99 levels of confidence. Provide the Critical Value, a sketch of the Critical Value, the Standard Error, and all formulas and calculations. Use technology for the sketch.

Answer to question 9: The c-value is 2.021 and also added a picture of the confidence interval i got as the answer.

Population mean: 10.6

Question I need answered is below:

Design a hypothesis test for the mean. Pick the same c-value selected in question 9. Provide a sketch of your solution. Your sketch should include critical values, test statistics, and p-value. Use technology for the sketch. Provide all formulas and any calculations. Use technology to justify the p-value found. You may use any method covered in class.

The 95% confidence interval is:

\[ CI = \bar{x} \pm t(s_e) \]

\[ = 10.585 \pm 2.021(0.485) \]

\[ = 10.585 \pm 0.98 \]

\[ \approx (9.605, 11.565) \]

This calculation involves finding the confidence interval for a sample mean. Here, $\bar{x}$ is the sample mean, $t$ is the t-value for the desired confidence level, and $s_e$ is the standard error of the mean. The resulting confidence interval is approximately from 9.605 to 11.565.

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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