5a. Several studies have shown that women with many children are less likely to

Question

5a. Several studies have shown that women with many children are less likely to get ovarian cancer. In a new study, data are collected from 25 women ages 40 – 49 with ovarian cancer. The mean parity (number of children) of these women is 1.8 with standard deviation 1.2. Suppose the mean number of children among women in the general population in this age group is 2.5. What test can be used to test the hypothesis that women with ovarian cancer have fewer children than women in the general population in the same age group

b. Perform the test mentioned in 5a using the 5 step hypothesis method

Explanation / Answer

The hypothesis formulation is

H0 : women with ovarian cancer do not have fewer children than women in the general population in the same age group   

H1 : women with ovarian cancer have fewer children than women in the general population in the same age group   

given that

xbar = 1.8 , n = 25 , sd = 1.2

and mu = 2.5

we know that the t stat is

t = (xbar-mu)/(sd/sqrt(n))

= (1.8-2.5)/(1.2/sqrt(25)) = -2.916

now we check the crtitical value from the t table using the df = n-1 = 25-1 = 24

and alpha = 0.05 , please note that this is a one tail test as we are interested in the fewer than part . we check the t table for the p value

The P-Value is .003839.

The result is significant at p < .05

hence we reject the null hypothesis in favor of alternate hypothesis to conclude that women with ovarian cancer have fewer children than women in the general population in the same age group

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