What type of person is most involved in the neighborhood and community? Who is more likely to volunteer for organizations such as PTA, scouts, or Little League? A random sample of 12 people have been asked for their number of memberships in community voluntary organizations and the number of children in their family. Test whether membership varies as a function of number of children using the .05 level of significance. Correct decision and conclusion? No Children One Child More Than One Child 2 1 3 3 M1=1.60 M2=3.40 M3=? S1=1.34 S2=0.89 S3=? Group of answer choices Decision: Reject the null hypothesis; Conclusion: Families that have no children have a lower mean number of memberships compared to families with one child or more than one child Decision: Reject the null hypothesis; Conclusion: Families that have no children, one child, or more than one child differ in terms of the mean number of memberships Decision: Do not reject the null hypothesis; Conclusion: Families that have no children, one child, or more than one child do not differ in terms of the mean number of memberships Decision: Do not reject the null hypothesis; Conclusion: Families that have one child or more than one child are virtually identical in terms of mean number of memberships

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Description: What type of person is most involved in the neighborhood and community? Who is more likely to volunteer for organizations such as PTA, scouts, or Little League? A random sample of 12 people have been asked for their number of memberships in community

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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What type of person is most involved in the neighborhood and community? Who is more likely to volunteer for organizations such as PTA, scouts, or Little League? A random sample of 12 people have been asked for their number of memberships in community voluntary organizations and the number of children in their family. Test whether membership varies as a function of number of children using the .05 level of significance.

Correct decision and conclusion?

No Children	One Child	More Than One Child
		2
		1
		3
		3
M₁=1.60	M₂=3.40	M₃=?
S₁=1.34	S₂=0.89	S₃=?

Group of answer choices

Decision: Reject the null hypothesis; Conclusion: Families that have no children have a lower mean number of memberships compared to families with one child or more than one child

Decision: Reject the null hypothesis; Conclusion: Families that have no children, one child, or more than one child differ in terms of the mean number of memberships

Decision: Do not reject the null hypothesis; Conclusion: Families that have no children, one child, or more than one child do not differ in terms of the mean number of memberships

Decision: Do not reject the null hypothesis; Conclusion: Families that have one child or more than one child are virtually identical in terms of mean number of memberships

Expert Solution

Step 1

Given:

Number of groups = k = 3,

Total sample size = N = 12.

Step 2

$M_{3} = \frac{2 + 1 + 3 + 3}{4} = 2.25 S_{3} = \sqrt{\frac{{(2 - 2.25)}^{2} + {(1 - 2.25)}^{2} + {(3 - 2.25)}^{2} + {(3 - 2.25)}^{2}}{4 - 1}} = 0.96$

Grand mean:

$x_{G} = \frac{(1.60 \times 4) + (3.40 \times 4) + (2.25 \times 4)}{12} = 2.42$

Treatment sum of squares:

$\begin{array}{rcl} S S R & = & [4 \times {(1.60 - 2.42)}^{2}] + [4 \times {(3.40 - 2.42)}^{2}] + [4 \times {(2.25 - 2.42)}^{2}] \\ = & 2.6896 + 3.8416 + 0.1156 \\ = & 2.92 \end{array}$

Error sum of squares:

$\begin{array}{rcl} S S E & = & S_{1} + S_{2} + S_{3} \\ = & 1.34 + 0.89 + 0.96 \\ = & 3.19 \end{array}$

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