(a) Use the p-value approach. A goodness of fit test will be conducted for the following hypotheses. This type of test is always an upper tail test. The p-value approach will be used, meaning that the given level of significance, a = 0.01, will be compared to the area under the curve to the right of the calculated test statistic. = 0.40, PB = 0.40, and Pc = 0.20 Ho:PA Ha: The population proportions are not på = 0.40, PB = 0.40, and pc = 0.20. The goal of the hypothesis test is to determine if the observed proportions are significantly different from the given proportions. A sample size of 200 yielded 20 in category A, 160 in category B, and 20 in category C. Assuming the hypothesized proportions are true, then the expected frequencies in each category will be the product of the hypothesized proportions and the sample size. expected frequency = category proportion(sample size) The proportion for category A is assumed to be 0.40. Use the sample size of 200 to find the expected frequency for this category, e4. expected frequency = category proportion(sample size) (200) %3D The proportion for category B is assumed to be 0.40. Use the sample size of 200 to find the expected frequency for this category, eg. expected frequency = category proportion(sample size) )(200) eB = %3D The proportion for category C is assumed to be 0.20. Use the sample size of 200 to find the expected frequency for this category, ec. expected frequency = category proportion(sample size) ec = (200) %3D

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) Use the p-value approach.
A goodness of fit test will be conducted for the following hypotheses. This type of test is always an upper tail
test. The p-value approach will be used, meaning that the given level of significance, a = 0.01, will be
compared to the area under the curve to the right of the calculated test statistic.
Ho:PA = 0.40, PB = 0.40, and Pc
Ha: The population proportions are not pa = 0.40, pB = 0.40, and Pc
= 0.20
%3D
0.20.
%3D
%D
The goal of the hypothesis test is to determine if the observed proportions are significantly different from the
given proportions. A sample size of 200 yielded 20 in category A, 160 in category B, and 20 in category C.
Assuming the hypothesized proportions are true, then the expected frequencies in each category will be the
product of the hypothesized proportions and the sample size.
expected frequency = category proportion(sample size)
The proportion for category A is assumed to be 0.40. Use the sample size of 200 to find the expected
frequency for this category, ea:
expected frequency
= category proportion(sample size)
)(200)
%3D
The proportion for category B is assumed to be 0.40. Use the sample size of 200 to find the expected
frequency for this category, eg.
expected frequency
category proportion(sample size)
eB =
|(200)
%D
The proportion for category C is assumed to be 0.20. Use the sample size of 200 to find the expected
frequency for this category, ec:
expected frequency
category proportion(sample size)
ec = (
(200)
%3D

Expert Solution

Step 1

Hypothesis:

$H_{0} : P_{A} = 0.40, P_{B} = 0.40 and P_{C} = 0.20 H_{1} : The population proportions are not P_{A} = 0.40, P_{B} = 0.40 and P_{C} = 0.20 .$

n=200

The expected frequency is calculated as below:

$\begin{array}{rcl} expected frequency & = & category proportion \times (sample size) \\ e_{A} & = & 0.40 \times 200 \\ = & 80 \\ e_{B} & = & 0.40 \times 200 \\ = & 80 \\ e_{C} & = & 0.20 \times 200 \\ = & 40 \end{array}$

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