A study was conducted to determine the proportion of people who dream in black a

Question

A study was conducted to determine the proportion of people who dream in black and white instead of color. Among 321 people over the age of 55, 68 dream in black and white, and among 307 people under the age of 25, 10 dream in black and white. Use a 0.05 significance level to test the claim that the proportion of people over 55 who dream in black and white is greater than the proportion for those under 25. Complete parts (a) through (c) below. identify test statistiz Z=? pvalue? and a 90% interval <P1-P2<

Explanation / Answer

n1 = 321 x1= 68 p1=x1/n1=68/321=0.2118 q1 = 1-0.2118=0.7882

n2=307 x2= 10 p2=x2/n2=10/307=0.0325 q2= 1-0.0325 = 0.9675

alpha a=0.05

a) z=(p1-p2)/sqrt {(p1*(q1)/n1 +(p2)*(q2)/n2}
z= (0.2118-0.0325)/sqrt {(0.7882*0.2118) /321 +(0.0325*0.9675)/307}

z=0.1793/ sqrt(0.0005+0.0001)

z= =7.319

b)

This is highly significant with p<0.0001
The null hypothesis is rejected.

c) p^-E <P1-P2<P^+E

WHERE E = Za/2 * (sqrt qrt {(p1*(q1)/n1 +(p2)*(q2)/n2}

   =1.645 *( 0.0244) = 0.0401

0.1793-0.0401 <P1-P2 <0.1793+0.0401

0.1392<P1-P2<0.2194

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