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
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