Question

1. 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 105 women and 115 men reveal that 7 women and 18 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=.025?

   For the hypothesis stated above, what is the test statistic (in terms of "Women" minus "Men")?

   	a.	-2.1537
   	b.	None of the answers is correct
   	c.	-2.1352
   	d.	-2.1141
   	e.	-2.0975

Answer 1

Solution :

Given that,

n1 = 105

x1 = 7

Point estimate = sample proportion = 1 = x1 / n1 = 0.067

n2 = 115

x2 = 18

Point estimate = sample proportion = 2 = x2 / n2 = 0.157

The value of the pooled proportion is computed as,

= ( x1 + x2 ) / ( n1 + n2 )

= (7 + 18 ) / (105 + 115 )

= 0.114

1 - = 0.886

Level of significance = = 0.025

This a two-tailed test.

The null and alternative hypothesis is,

Ho: p1 = p2

Ha: p1 p2

Test statistics

z = (1 - 2 ) / *(1-) ( 1/n1 + 1/n2 )

= (0.067 - 0.157 ) / (0.114 * 0.886 ) (1/105 + 1/115 )

= -2.0975

Option e) is correct.

P-value = 2 * P(Z < z )

= 2 * P(Z < -2.0975 )

= 2 * 0.0180

= 0.036

The p-value is p = 0.036, and since p = 0.036 > 0.025, it is concluded that fail to reject the null hypothesis.