Question

1.) Estimate with 95% confidence the change in the population proportion from the first survey to the second survey that were obese and interpret the results.

Q: The Tomz Store takes periodic randomized surveys to track health of Americans. In a survey of 4881 adults in 2007-2008, 1674 were obese (body mass index BMI ≥ 30). In a survey of 5181 adults in 2011-2012, 1808 were obese.

Answer 1

95% confidence the change in the population proportion from the first survey:

The sample proportion is computed as follows, based on the sample size N = 4881 and the number of favorable cases X = 1674: X N 1674 4881 = 0.343 The critical value for a = 0.05 is ze = 21-a/2 = 1.96. The corresponding confidence interval is computed as shown below: p(1-7) p(1 - ) CI(Proportion) = P - 21 P + 2CV n n 0.343 - 1.96 x 0.343(1 -0.343) ,0.343 +1.96 x 4881 0.343(1 -0.343) 4881 = (0.33, 0.356) Therefore, based on the data provided, the 95% confidence interval for the population proportion is 0.33 <p <0.356, which indicates that we are 95% confident that the true population proportion pis contained by the interval (0.33, 0.356).

95% confidence the change in the population proportion from the second survey:

The sample proportion is computed as follows, based on the sample size N = 5181 and the number of favorable cases X = 1808: p X N 1808 5181 = 0.349 1.96. The corresponding confidence interval is The critical value for a = 0.05 is ze = 21-a/2 computed as shown below: CI(Proportion) p(1-) p(1 - ) Ô - ZV P +2c ZcV n n = 0.349 - 1.96 x 0.349(1 -0.349) ,0.349 +1.96 x 5181 0.349(1 -0.349) 5181 (0.336,0.362) Therefore, based on the data provided, the 95% confidence interval for the population proportion is 0.336 <p <0.362, which indicates that we are 95% confident that the true population proportion p is contained by the interval (0.336,0.362).