News reports speak of an emerging crisis of childhood obesity in the United Stat
ID: 3225216 • Letter: N
Question
News reports speak of an emerging crisis of childhood obesity in the United States. The National Health and Nutrition Examination Survey (NHANES) is a government survey run every several years recording a number of vital statistics on a random sample of Americans. A body mass index (BMI) is computed for each individual in the sample based on the individual's height and weight. Here are sample results for 8-year-old boys over the past 40 years The table gives the sample size for 3 different surveys, the sample mean and sample standard deviation. Suppose we want to run an ANOVA to see if there is a difference in mean BMI for the three surveys. Assume each survey is a random sample and there are no extreme outliers. (a) The distribution of BMI from each survey is somewhat right-skewed. Is the Normality condition met for an ANOVA on this data? Why? Yes, because the data was randomly gathered Yes, because the ANOVA procedures are robust to skewness for sample sizes over 30 and there are no extreme outliers No, because skewness violates the Normality condition even when the sample sizes are over 30 (b) What is the sample standard deviations for each survey? the NHES II study? (Use 3 decimal places) the NHANES II study? (Use 3 decimal places) the NHANES study? (Use 3 decimal places) (c) Do the standard deviations satisfy the guidelines for the use of ANOVA? No, because the largest standard deviation is has than twice the smallest standard deviation No, because the largest standard deviation is mote than twice the smallest standard deviation Yes, because the largest standard deviation is less than twice the smallest standard deviation Yes, because the largest standard deviation is mote than twice the smallest standard deviation.Explanation / Answer
A.a) No because skewness violates the normality condition even when the sample sizes are over 30
A.b) the sample standard deviation for each survey are
NHES II study= 2.486
NHANES II study= 2.408
NHANES study= 5.851
A.c) NO, because the largest sample SD is more than twicce larger than the smallest SD