a)Compute the sample proportion of Yes responses for each population. The sample proportion, p, of the Yes responses for each population will be calculated using the Yes and No responses for the respective population as follows. sample proportion = yes responses yes and no responses Recall the given data. Observed Frequencies (fij) Response Populations 1 2 3 Yes 132 132 78 No 118 168 122 Let p1 represent the sample proportion of Yes responses for population 1, p2 represent the sample proportion of Yes responses for population 2, and p3 represent the sample proportion of Yes responses for population 3. Find the sample proportions. p1 = 132 132 132 + 118 = .528 0.528 p2 = 132 132 132 + 168 = .44 0.44 p3 = 78 78 78 + 122 = .39 0.39 Step 2 (b)Use the multiple comparison procedure to determine which population proportions differ significantly. Use a 0.05 level of significance. A multiple comparison procedure is done to determine if any two populations are significantly different from one another. This procedure can be done when there are at least 3 populations being compared. The first step is to compute the absolute value of each of the differences, |pi − pj|, for populations i and j. We previously found the following sample proportions. p1 = 0.528 p2 = 0.44 p3 = 0.39 Find the absolute value of the difference in population proportions for populations i = 1 and j = 2. |p1 − p2| = 0.528 − .44 0.44 = .088 0.088 Find the absolute value of the difference in population proportions for populations i = 1 and j = 3. |p1 − p3| = 0.528 − .39 0.39 = .138 0.138 Find the absolute value of the difference in population proportions for populations i = 2 and j = 3. |p2 − p3| = 0.44 − .39 0.39 = .05 0.05 Step 3 The next step in the multiple comparison procedure is to compute a critical value for each pairwise comparison. The critical value for the ij pairwise difference for k populations follows where ??2 is the chi-square value with level of significance ? and k − 1 degrees of freedom for k populations, pi and pj are the sample proportions for populations i and j, and ni and nj are the sample sizes from populations i and j. CVij = ??2 pi(1 − pi) ni + pj(1 − pj) nj The value for ??2 will be used for all comparisons. Note that ? will represent the upper tail area of the chi-square distribution. The desired level of significance was given to be 0.05, so ? = . There are three populations being compared, giving k = . Population 1 had 132 Yes responses and 118 No responses. Therefore, n1 = 132 + 118 = . Population 2 had 132 Yes responses and 168 No responses. Therefore, n2 = 132 + 168 = . Population 3 had 78 Yes responses and 122 No responses. Therefore, n3 = 78 + 122 = .

a)Compute the sample proportion of Yes responses for each population. The sample proportion, p, of the Yes responses for each population will be calculated using the Yes and No responses for the respective population as follows. sample proportion = yes responses yes and no responses Recall the given data. Observed Frequencies (fij) Response Populations 1 2 3 Yes 132 132 78 No 118 168 122 Let p1 represent the sample proportion of Yes responses for population 1, p2 represent the sample proportion of Yes responses for population 2, and p3 represent the sample proportion of Yes responses for population 3. Find the sample proportions. p1 = 132 132 132 + 118 = .528 0.528 p2 = 132 132 132 + 168 = .44 0.44 p3 = 78 78 78 + 122 = .39 0.39 Step 2 (b)Use the multiple comparison procedure to determine which population proportions differ significantly. Use a 0.05 level of significance. A multiple comparison procedure is done to determine if any two populations are significantly different from one another. This procedure can be done when there are at least 3 populations being compared. The first step is to compute the absolute value of each of the differences, |pi − pj|, for populations i and j. We previously found the following sample proportions. p1 = 0.528 p2 = 0.44 p3 = 0.39 Find the absolute value of the difference in population proportions for populations i = 1 and j = 2. |p1 − p2| = 0.528 − .44 0.44 = .088 0.088 Find the absolute value of the difference in population proportions for populations i = 1 and j = 3. |p1 − p3| = 0.528 − .39 0.39 = .138 0.138 Find the absolute value of the difference in population proportions for populations i = 2 and j = 3. |p2 − p3| = 0.44 − .39 0.39 = .05 0.05 Step 3 The next step in the multiple comparison procedure is to compute a critical value for each pairwise comparison. The critical value for the ij pairwise difference for k populations follows where ??2 is the chi-square value with level of significance ? and k − 1 degrees of freedom for k populations, pi and pj are the sample proportions for populations i and j, and ni and nj are the sample sizes from populations i and j. CVij = ??2 pi(1 − pi) ni + pj(1 − pj) nj The value for ??2 will be used for all comparisons. Note that ? will represent the upper tail area of the chi-square distribution. The desired level of significance was given to be 0.05, so ? = . There are three populations being compared, giving k = . Population 1 had 132 Yes responses and 118 No responses. Therefore, n1 = 132 + 118 = . Population 2 had 132 Yes responses and 168 No responses. Therefore, n2 = 132 + 168 = . Population 3 had 78 Yes responses and 122 No responses. Therefore, n3 = 78 + 122 = .

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

See similar textbooks

a)Compute the sample proportion of Yes responses for each population.

The sample proportion,

of the Yes responses for each population will be calculated using the Yes and No responses for the respective population as follows.

sample proportion =

yes responses

yes and no responses

Recall the given data.

Observed Frequencies

(f_ij)

Response	Populations
1	2	3
Yes	132	132	78
No	118	168	122

Let

p₁

represent the sample proportion of Yes responses for population 1,

p₂

represent the sample proportion of Yes responses for population 2, and

p₃

represent the sample proportion of Yes responses for population 3. Find the sample proportions.

p₁

132

132 + 118

.528

0.528

p₂

132

132 + 168

.44

0.44

p₃

78 + 122

.39

0.39

Step 2

(b)Use the multiple comparison procedure to determine which population proportions differ significantly. Use a 0.05 level of significance.

A multiple comparison procedure is done to determine if any two populations are significantly different from one another. This procedure can be done when there are at least 3 populations being compared. The first step is to compute the absolute value of each of the differences,

|p_i − p_j|,

for populations i and j. We previously found the following sample proportions.

p₁ = 0.528

p₂ = 0.44

p₃ = 0.39

Find the absolute value of the difference in population proportions for populations

i = 1

and

j = 2.

|p₁ − p₂|

0.528 − .44

0.44

.088

0.088

Find the absolute value of the difference in population proportions for populations

i = 1

and

j = 3.

|p₁ − p₃|

0.528 − .39

0.39

.138

0.138

Find the absolute value of the difference in population proportions for populations

i = 2

and

j = 3.

|p₂ − p₃|

0.44 − .39

0.39

.05

0.05

Step 3

The next step in the multiple comparison procedure is to compute a critical value for each pairwise comparison. The critical value for the ij pairwise difference for k populations follows where

?_?²

is the chi-square value with level of significance ? and

k − 1

degrees of freedom for k populations,

p_i

and

p_j

are the sample proportions for populations i and j, and

n_i

and

n_j

are the sample sizes from populations i and j.

CV_ij =

?_?²

p_i(1 − p_i)

n_i

p_j(1 − p_j)

n_j

The value for

?_?²

will be used for all comparisons. Note that ? will represent the upper tail area of the chi-square distribution. The desired level of significance was given to be 0.05, so ? = . There are three populations being compared, giving k = .

Population 1 had 132 Yes responses and 118 No responses. Therefore,

n₁ = 132 + 118 = .

Population 2 had 132 Yes responses and 168 No responses. Therefore,

n₂ = 132 + 168 = .

Population 3 had 78 Yes responses and 122 No responses. Therefore,

n₃ = 78 + 122 = .

Expert Solution

Trending now

This is a popular solution!

Step by step

Solved in 2 steps with 1 images

SEE SOLUTION Check out a sample Q&A here

Knowledge Booster

$Research Ethics$

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, statistics and related others by exploring similar questions and additional content below.