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Name: A psychologist specializing in marriage counseling claims that, among
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Description: A psychologist specializing in marriage counseling claims that, among all married couples, the proportion p for whom her communication program can prevent divorce is at least 79% . In a random sample of 245 married couples who completed her program,1

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 psychologist specializing in marriage counseling claims that, among all married couples, the proportion p for whom her communication program can prevent divorce is at least 79% . In a random sample of 245 married couples who completed her program,180 of them stayed together. Based on this sample, can we reject the psychologist's claim at the 0.05 level of significance?

Perform a one-tailed test. Then complete the parts below.

Carry your intermediate computations to three or more decimal places and round your answers as specified in the table.

(a)	State the null hypothesis H0? and the alternative hypothesis H1? .
H0:?
H1:?
(b)	Determine the type of test statistic to use.
	▼(Choose one) z ? t ? chi square ? f ?
(c)	Find the value of the test statistic?. (Round to three or more decimal places.)

(d)	Find the p-value.? (Round to three or more decimal places.)

(e)	Can we reject the psychologist's claim that the proportion of married couples for whom her program can prevent divorce is at least 79% ?
Yes or No?

Expert Solution

Step 1

Solution:

Given information:

n= 245 Sample size of married couple

x= 180 married couple stayed together

$\hat{p} = \frac{x}{n} = \frac{180}{245} = 0.7346938 \hat{p} = 0.7347 S a m p l e p r o p o r t i o n o f m a r r i e d c o u p l e s t a y t o g e t h e r$

p = 0.79 Population proportion

$α = 0.05 L e v e l o f s i g n i f i c a n c e$

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