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Name: A neighborhood of 45 homes found that 75% (SD=2.1) had at least one pe
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Description: A neighborhood of 45 homes found that 75% (SD=2.1) had at least one pet. The city-wide average for neighborhoods is 71%. Find the critical value of t and the value of t we obtain (or observe) presuming a 2-tailed test. Also, calculate the effect size

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 neighborhood of 45 homes found that 75% (SD=2.1) had at least one pet. The city-wide average for neighborhoods is 71%. Find the critical value of t and the value of t we obtain (or observe) presuming a 2-tailed test. Also, calculate the effect size. Lastly, write a statement of the hypotheses with your findings.

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$\begin{array}{rcl} \bar{x} & = & S a m p l e m e a n \\ = & 75 \end{array}$

$\begin{array}{rcl} s & = & S a m p l e S . D \\ = & 2.1 \end{array}$

$\begin{array}{rcl} n & = & S a m p l e s i z e \\ = & 45 \end{array}$

The null hypothesis is $H_{0} : μ = 71$

Tested against the alternative hypothesis $H_{1} : μ \neq 71$ .

The test statistic is

$\begin{array}{rcl} t & = & \frac{\bar{x} - μ}{\frac{s}{\sqrt{n - 1}}} \\ = & \frac{75 - 71}{\frac{2.1}{\sqrt{45 - 1}}} \\ = & 12.6348 \end{array}$

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