Question 960762
<pre>

A)

H<sub>0</sub>: p<sub>1</sub> = p<sub>2</sub>
H<sub>a</sub>: p<sub>1</sub> &#8800; p<sub>2</sub>

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B)

The rejection region will be 

|z| > 1.96  or if you prefer z < -1.96 or z > 1.96  

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(C)
</pre>
At the end of the study, 38% of the women caught a cold, and 51% of the men caught a cold.
<pre>

Since we are testing effectiveness in preventing a cold, not in catching a
cold, we subtract from 100% and consider this as saying that 62% of the women 
did not catch a cold, and that 49% of the men did not catch a cold.

Since there were 100 women, then {{{x[1]=(0.62)(100)}}} or 62 women did not
catch cold.

Since there were 200 men, then {{{x[2]=(0.49)(200)}}} or 98 men did not
catch cold. 

{{{drawing(200,200,-5,5,-5,5,

locate(-4.5,3.2,"^"),locate(-4.5,1.35,"^"),

locate(-4.5,3.7,

matrix(4,1,

p[1]=0.62,
p[2]=0.49,
n[1]=100,
n[2]=200)
 ) )  )}}}


{{{drawing(300,100,-5,5,-5,5,locate(-4.5,.9,"^"),

locate(-4.5,3.7,

p=(x[1]+x[2])/(n[1]+n[2])=(62+98)/(100+200)=160/300=0.5333))}}}

Substitute those values in the formula below to find z.

{{{drawing(200,200,-5,5,-5,5,locate(-4.5,1.5,z),locate(-4,1.45,""=""),
locate(-.4,2.56,"^"),locate(1,2.56,"^"),
locate(-2.1,-.27,"^"),locate(-.25,-.27,"^"),
locate(-3,3,(p[1]-p[2])/( sqrt(p^""(1-p))sqrt(1/n[1]+1/n[2]))) )}}}

{{{z}}}{{{""=""}}}{{{(0.62-0.49)/( sqrt(0.5333^""(1-0.5333))sqrt(1/100+1/200))=2.1276}}}

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(D)

2.1276 is greater than 1.96, so we reject the null hypothesis.

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(E)

There is a significant difference between the effectiveness of the new drug
for cold prevention in women and its effectiveness for cold prevention in men.   

Edwin</pre>