Question

Philip Morris wishes to determine if there is a difference between the proportion of women and proportion of men who smoke cigarettes. Random samples of 120 women and 110 men reveal that 8 women and 16 men smoke cigarettes. Does the data indicate that the proportion of women who smoke cigarettes is lower than the proportion of men who do at α=.05?

What is the 99% confidence interval for p_Women - p_Men?

	a.	None of the answers is correct
	b.	(-0.1734, 0.0158)
	c.	(-0.1827, 0.0251)
	d.	(-0.1728, 0.0152)
	e.	(-0.1833, 0.0258)

Answer 1

1)

n1=120, n2=110

x1=8, x2=16

Ho: P1 = P2

Ha: P1 < P2

Z = -1.95

P-Value = P(z < -1.95)

using normal z table we get

P(z < -1.95) = 0.0256

P-Value = 0.0256

decision rule is

Reject Ho if ( P-value ) ( )

here, ( P-value= 0.0256 ) < ( = 0.05)

Hence, we can say,

Null hypothesis is rejected.

There is sufficient evidence to  support the claim that the proportion of women who smoke cigarettes is lower than the proportion of men who do at α=.05

2)

c= 99%

formula for confidence interval is

Where Zc is the z critical value for c=99%

Zc= 2.58

-0.1833 < P1 - P2 <   0.0258

e. (-0.1833, 0.0258)