Math Problem Statement
A body mass index (BMI) between 20 and 25 indicates a normal weight. In a random survey of 783 people from Group A and 780 people from Group B, it was found that 269 people from Group A and 294 people from Group B were normal weight. Construct a 90% confidence interval of the difference in the proportion of people from Group A and people from Group B who are normal weight. Then interpret the interval.
Note the subscripts a and b represent people from Group A and people from Group B, respectively. Therefore sample 1 is the people from Group A and sample 2 is the people from Group B.
Incorrect < p a − p b <
Round each answer to 4 decimal places.
Solution
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Math Problem Analysis
Mathematical Concepts
Statistics
Confidence Intervals
Proportions
Formulas
Sample proportion: \( \hat{p} = \frac{x}{n} \)
Standard Error for proportions: \( SE = \sqrt{\frac{\hat{p}_a(1 - \hat{p}_a)}{n_a} + \frac{\hat{p}_b(1 - \hat{p}_b)}{n_b}} \)
Confidence interval: \( (\hat{p}_a - \hat{p}_b) \pm z \times SE \)
Theorems
Central Limit Theorem
Suitable Grade Level
College/Advanced High School
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