Question

Body Mass Index (BMI) is a number calculated from a person's weight and height and is calculated by the formula: weight (kg) / [height (m)]2. Though somewhat controversial and not meant to be used as a diagnostic criteria, it can be used to characterize body type and (with caution) fitness and health using readily available data. Commonly accepted classifications are listed below: • Below 18.5 is underweight; • 18.5 to 25 is normal; • 25 to 30 is overweight; • Above 30 is obese. 5. Another study is conducted to estimate the average BMI for middle-age US females. The study includes a random sample of 21 middle-aged US females with a sample mean of 24 and a sample standard deviation of a) Is it safe to assume the sampling distribution of BMI for 21 randomly selected females approximately normal? Why or why not? b) Use the appropriate formula to construct a 95% CI for the true mean BMI for middle-aged US females.

Answer 1

a) We cannot assume the sampling distribution of BMI for 21 randomly selected females is approximately normal, as the sample size is small. b) To construct a 95% Confidence Interval for the true mean BMI, we use the t-distribution and the formula CI = sample mean ± (critical value) * (sample standard deviation / √n).

Step-by-step explanation:

a) In order to determine if it is safe to assume the sampling distribution of BMI for 21 randomly selected females is approximately normal, we need to check if the sample size is large enough and if the population distribution is approximately normal. Since the sample size is small (n=21), we cannot assume a normal distribution unless the population distribution is also normal.

b) To construct a 95% Confidence Interval (CI) for the true mean BMI for middle-aged US females, we can use the formula: CI = sample mean ± (critical value) * (sample standard deviation / √n). Since the population standard deviation is unknown, we should use the t-distribution and the corresponding critical value.

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