1. Nine hundred (900) teenage boys and 1500 teenage girls were randomly selected for a STEPS survey in Trinidad and Tobago in 2017. STEPS surveys are regularly carried out in Trinidad and Tobago to identify the major risk factors that determine the major diseases burden among teenagers. The mean BMI among the boys sample is 21.85, while the mean BMI among the sample of girls is 22.39. The corresponding sample standard deviations for the two groups of teenagers are 5.90 and 6.39, respectively. Given that 81 of the sample of teenage boys and 144 of the sample of teenage girls have BMI that are greater than 30.5, test the hypothesis (at the 5% level) that the population proportions of teenage boys and teenage girls with BMI that are greater than 30.5 are the same.
1. Nine hundred (900) teenage boys and 1500 teenage girls were randomly selected for a STEPS survey in Trinidad and Tobago in 2017. STEPS surveys are regularly carried out in Trinidad and Tobago to identify the major risk factors that determine the major diseases burden among teenagers. The mean BMI among the boys sample is 21.85, while the mean BMI among the sample of girls is 22.39. The corresponding sample standard deviations for the two groups of teenagers are 5.90 and 6.39, respectively.
Given that 81 of the sample of teenage boys and 144 of the sample of teenage girls have BMI that are greater than 30.5, test the hypothesis (at the 5% level) that the population proportions of teenage boys and teenage girls with BMI that are greater than 30.5 are the same.
Given:
Sample size of teenage boys (n1) = 900
Sample size of teenage girls (n2)= 1500
Number of people in the sample of teenage boys with BMI greater than 30.5 (x1) = 81
Number of people in the sample of teenage boys with BMI greater than 30.5 (x2) = 144
α = 0.05
Let population proportion of teenage boys with BMI greater than 30.5 be p1.
Let population proportion of teenage girls with BMI greater than 30.5 be p2.
Step by step
Solved in 3 steps with 4 images
