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 110 women and 95 men reveal that 14 women and 7 men smoke cigarettes. Does the data indicate that the proportion of women who smoke cigarettes is higher than the proportion of men who do at α=.005? For the hypothesis stated above, what is the test statistic (in terms of "Women" minus "Men")?
a. (-0.0279,0.1351).
b. (-0.0297,0.1368).
c. (-0.0148, 0.1220).
d. (-0.0163, 0.1235).
e. none of these is correct.

Answer 1

Answer:

Step-by-step explanation:

This is a test of 2 population proportions. Let 1 and 2 be the subscript for the women and men who smoke respectively. The population proportion of women and men who smoke would be p1 and p2 respectively.

p1 - p2 = difference in the proportion of women and men who smoke.

The null hypothesis is

H0 : p1 = p2

p1 - p2 = 0

The alternative hypothesis is

Ha : p1 > p2

p1 - p2 > 0

it is a right tailed test

Sample proportion = x/n

Where

x represents number of success(number of complaints)

n represents number of samples

For women

x1 = 14

n1 = 110

p1 = 14/110 = 0.13

For men,

x2 = 7

n2 = 95

p2 = 7/95 = 0.07

The pooled proportion, pc is

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

pc = (14 + 7)/(110 + 95) = 0.1

1 - pc = 1 - 0.1 = 0.9

z = (p1 - p2)/√pc(1 - pc)(1/n1 + 1/n2)

z = (0.13 - 0.07)/√(0.1)(0.9)(1/110 + 1/95)

z = 1.47

From the options given, the test statistic is

e. none of these is correct.

Since it is a right tailed test, we will look at the area to the right of z = 1.47. The p value would be

p value = 1 - 0.9292 = 0.078

Since alpha, 0.005 < than the p value, 0.078, then we would fail to reject the null hypothesis. Therefore, the data does not indicate that the proportion of women who smoke cigarettes is higher than the proportion of men who do at α=.005