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.