6.127 Food selection by children in school cafeterias. A group of researchers examined whether children’s food selection in a school cafeteria met the standards set by the School Meals Initiative. They measured food selection and food intake of 2049 fourth- through sixth-grade students in 33 schools over a three-day period using digital photography. The following table summarizes some of the food intake measurements.31
| Boys | Girls | |||
|---|---|---|---|---|
| n = 852 | n = 1197 | |||
| Food intake | Mean | St. Dev. | Mean | St. Dev. |
| Energy (kilojoules) | 2448 | 717 | 2170 | 693 |
| Protein (g) | 24.5 | 7.5 | 22.1 | 7.7 |
| Calcium (mg) | 324.1 | 130.6 | 265.0 | 128.9 |
Given the large sample sizes, we can assume that the sample standard deviations are the population standard deviations.
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(a) Compute 95% confidence intervals for all three intake measures for the boys.
(b) Compute 95% confidence intervals for all three intake measures for the girls.
(c) In the next chapter, we will describe the confidence interval for the difference between two means. For now, let’s compare the boy and girl confidence intervals for each food intake measure. Do you think these pairs of intervals provide strong evidence against the null hypothesis that the boys and girls consume, on average, the same amount? Explain your answer.