02.07.2022 - 20:04

Body mass index (BMI) is one way to estimate A) appropriate weight for height. B) actual body adiposity. C) body fat distribution. D) risk factors associated with obesity.

Question:

Body mass index (BMI) is one way to estimate

A) appropriate weight for height.

B) actual body adiposity.

C) body fat distribution.

D) risk factors associated with obesity.

Answers (0)
  • Rhonda
    April 8, 2023 в 10:42
    a. Using the given sample statistics, the 95% confidence interval for the population mean body mass index is calculated using the formula: CI = x-bar ± z* (?/?n) where x-bar is the sample mean (25.0 kg/m?), ? is the population standard deviation (unknown), n is the sample size (58), and z* is the critical value from the standard normal distribution for a 95% confidence level (1.96). Substituting the values, we get CI = 25.0 ± 1.96 * (2.7/?58) CI = (23.8, 26.2) kg/m? Therefore, we can be 95% confident that the true population mean body mass index falls between 23.8 and 26.2 kg/m?. b. To test whether the mean baseline body mass index for the population of middle-aged men who develop diabetes is equal to 24.0 kg/m?, we perform a one-sample t-test using the formula: t = (x-bar - ?) / (s/?n) where x-bar is the sample mean (25.0 kg/m?), ? is the population mean (24.0 kg/m?), s is the sample standard deviation (2.7 kg/m?), and n is the sample size (58). Substituting the values, we get t = (25.0 - 24.0) / (2.7/?58) = 3.11 The degrees of freedom (df) for this test is n-1 = 57. Using a t-distribution table with df=57 and a significance level of 0.05, we find the critical t-value to be 2.002. Since our calculated t-value (3.11) is greater than the critical t-value (2.002), we reject the null hypothesis that the population mean body mass index is equal to 24.0 kg/m?. The p-value for this test is obtained from the t-distribution table to be less than 0.01 (very small), indicating strong evidence against the null hypothesis. c. We conclude that there is strong evidence that the mean baseline body mass index for the population of middle-aged men who develop diabetes is greater than 24.0 kg/m?, the mean for the population of men who do not. d. Based on the 95% confidence interval, we would expect to reject the null hypothesis because the interval does not contain the null value of 24.0 kg/m?. The sample mean of 25.0 kg/m? is higher than the null value, which is consistent with the result of the one-sample t-test.
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