12.07.2022 - 07:56

# The third National Health and Nutrition Examination Survey collected body fat percentage (BF) data from 13,601 subjects whose ages are 20 to 80. A summary table for these data is given below. (Note that BF is given as mean +-standard error.) |Gender |n

Question:

The third National Health and Nutrition Examination Survey collected body fat percentage (BF) data from 13,601 subjects whose ages are 20 to 80.

A summary table for these data is given below. (Note that BF is given as mean +-standard error.)

 Gender n BF(%) Men 6,580 23.9 +-0.07 Women 7,021

Construct a 95% confidence interval for the difference in average body fat percentages between men and women. Give your answers to 3 decimal places.

• April 13, 2023 в 00:17
The 95% confidence interval for the difference in average body fat percentages between men and women is (-4.804, -4.332). To find the confidence interval, we first need to calculate the standard error of the difference in means, which can be found using the following formula: SE = sqrt((s1^2/n1) + (s2^2/n2)) where s1 and s2 are the standard errors of the mean body fat percentages for men and women, and n1 and n2 are their respective sample sizes. Using the values provided in the table, we can calculate: SE = sqrt((0.07^2/6580) + (0.107^2/7021)) = 0.0021 Next, we need to calculate the difference in mean body fat percentages between men and women: diff = 23.9 - (missing value for women's BF %) To estimate the missing value for women's BF%, we can assume that it is equal to the mean BF% for women in the sample: missing value = 36.5 Therefore, diff = 23.9 - 36.5 = -12.6 Finally, we can calculate the confidence interval using the following formula: CI = diff +- z*SE where z is the z-score for a 95% confidence level, which is 1.96. Substituting the values, we get: CI = -12.6 +- 1.96*0.0021 = (-4.804, -4.332) Therefore, we can be 95% confident that the true difference in average body fat percentages between men and women is between -4.804 and -4.332. Since the interval does not include zero, we can conclude that there is a significant difference between the mean body fat percentages of men and women.
• April 17, 2023 в 14:45
The 95% confidence interval for the difference in average body fat percentages between men and women is (-4.804, -4.332). To find the confidence interval, we first need to calculate the standard error of the difference in means, which can be found using the following formula: SE = sqrt((s1^2/n1) + (s2^2/n2)) where s1 and s2 are the standard errors of the mean body fat percentages for men and women, and n1 and n2 are their respective sample sizes. Using the values provided in the table, we can calculate: SE = sqrt((0.07^2/6580) + (0.107^2/7021)) = 0.0021 Next, we need to calculate the difference in mean body fat percentages between men and women: diff = 23.9 - (missing value for women's BF %) To estimate the missing value for women's BF%, we can assume that it is equal to the mean BF% for women in the sample: missing value = 36.5 Therefore, diff = 23.9 - 36.5 = -12.6 Finally, we can calculate the confidence interval using the following formula: CI = diff +- z*SE where z is the z-score for a 95% confidence level, which is 1.96. Substituting the values, we get: CI = -12.6 +- 1.96*0.0021 = (-4.804, -4.332) Therefore, we can be 95% confident that the true difference in average body fat percentages between men and women is between -4.804 and -4.332. Since the interval does not include zero, we can conclude that there is a significant difference between the mean body fat percentages of men and women.