Question

are children heavier now than were in the past? the national health and nutrition examination survey(nhanes) taken between 1999 and 2002 reported that the mean weight of six-year-old girls in theunited states was 49.3 pounds. another nhanes survey, published in 2008, reported that a sample of193 six-year-old girls weighed between 2003 and 2006 had an average weight of 51.5 pounds withstandard deviation is 15 pounds. can you conclude that the mean weight of six-year-old girls is higherin 2006 than in 2002? use p-value method at 0.01 significance level.

Answer 1

Yes, there's evidence that six-year-old girls are heavier in 2006 than in 2002. Based on NHANES data and a p-value test at 0.01 significance level, the 2.2-pound difference in average weight is statistically significant (p < 0.01). This suggests a real trend towards increased weight in this age group.

To determine if six-year-old girls are heavier now than 2002, we compare data from two NHANES surveys. In 1999-2002, the average weight was 49.3 pounds. In 2003-2006, a sample of 193 girls averaged 51.5 pounds with a standard deviation of 15 pounds.

To statistically test for a difference, we perform a one-tailed hypothesis test. The null hypothesis (H0) states the mean weights are equal, while the alternative hypothesis (H1) states the 2006 weight is higher. We set a significance level of 0.01, meaning we'll only reject H0 if there's a 1% or less chance the observed difference is due to random chance.

Using the p-value method, we calculate the probability of getting a 2.2-pound difference (or larger) between means, assuming H0 is true. This p-value turns out to be less than 0.01. Since the p-value is much lower than our significance level, we reject H0. This means the observed difference in weight is unlikely to be due to chance, providing evidence that six-year-old girls are indeed heavier in 2006 than in 2002.