Do you have an insatiable craving for chocolate or some other food? Since many N

Question

Do you have an insatiable craving for chocolate or some other food? Since many North Americans apparently do, psychologists are designing scientific studies to examine the phenomenon. According to the New York Times (Feb. 22,1995), one of the largest studies of food cravings involved a survey of 1,000 McMaster University (Canada) students. The survey revealed that 97% of the women in the study acknowledged specific food cravings while only 67% of the men did. Assume that 600 of the respondents were women and 400 were men

a. Is there sufficient evidence to claim that the true proportion of women who acknowledge having food cravings exceeds the corresponding proportion of men? Test using a = .01

b. Why is it dangerous to conclude from the study that women have a higher incidence of food cravings than men?

show hypothesis testing!!!

Explanation / Answer

ans=

Ho: p1 </= p2
Ha: p1 > p2 (right tailed test)
Test statistic = z = [p1-p2] / SE
SE denotes the standard error of the difference between proportions
p1 = 97% = 0.97
p2 = 67% = 0.67
SE(p1-p2) = sqrt [p*q(1/n1 + 1/n2)]
p = [n1p1 + n2p2] / {n1+n2]
= [0.97*600 + 0.67*400] / [600+400]
= 0.85
q = 1-p = 1-0.85 = 0.15
SE = sqrt [0.85*0.15 (1/600 + 1/400)]
= 0.023
z = [0.97-0.67] / 0.023 = + 13.04
p-value applicable to right tailed test = P(Z>z)
= P(Z>13.04)
= 0.00000001
Since p-value < the alpha value, Ho will be rejected.
CHOICE (b) is NOT indicated properly
The answer is that ...
p1 can be said to be > p2 and the difference is statistically significant.

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