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Name: A random sample of 64 students from Wharton School was taken and their
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Description: A random sample of 64 students from Wharton School was taken and their GPA were recored. The sample mean GPA was 2.8 and the sample standard deviation was 0.5. The population size is 1200. a) Find the %99 confidence interval for the population varia

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 of 64 students from Wharton School was taken and their GPA were recored. The sample mean GPA was 2.8 and the sample standard deviation was 0.5. The population size is 1200.

a) Find the %99 confidence interval for the population variance.

b) Test at %8 significance level that null hypothesis being the population mean GPA is equal to 2.7 against the alternative it is not equal to 2.7. Suppose that population standard deviation is known to be 0.3 for this question. Compute the p-value.

c)Draw the figure showing the areas of Type 1 error, Type 2 error and p- value (it is not necessary to finde Type 2 error.)

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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