The body mass index BMI of an individual is a measure that i

The body mass index (BMI) of an individual is a measure that is used to judge whether an individual is overweight or not. A BMI between 20 and 25 indicates that one is at a normal weight. In a survey of 750 men and 750 women, the Gallup organization found that 203 men and 270 women were normal weight. Conduct a hypothesis testing whether there is a significant difference in the proportion of men and women who are normal weight at the significance level of 0.10. Interpret the result in terms of the context of problem. Construct a 90% confidence interval of the difference between the two population proportions of men and women, p_men - P_women. Interpret the result interval in practical way.

Solution

Given n1=n2=750, x1=203,x2=270, then p1=(203/750)=.2707, p2=(270/750)=.36, P=(473/1500)=.3153 & Q=1-P=.6847. Then Zcal=((.36-.2707)/(.3153*.6847*.0027))=3.7208 and Z table value at.10 level of significance is 1.645, Zcal>Ztab, so we reject null hypothesis i.e., there is a significant difference in the proportion of men and women. The 90% confidence interval of the difference between the two population proportion of men and women is (-0.1288,-0.0498).