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Nutritionists wish to estimate the difference in caloric intake at lunch between children in a school...

Nutritionists wish to estimate the difference in caloric intake at lunch between children in a school offering a hot school lunch program and children in a school which does not. From other nutrition studies, they estimate that the standard deviation in caloric intake among elementary school children is 75 calories, and they wish to make their estimate to within 20 calories of the true difference with 95% confidence.

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Answer #1

Suppose, random variable X denotes difference in caloric intake at lunch between children in a school offering a hot school lunch program and children in a school which does not.

We know,

Here,

Level of significance

[Using R-code 'qnorm(1-0.025)']

Standard deviation

Margin of error

Hence, at least 55 samples are required so that their estimate is within 20 calories of the true difference with 95% confidence.

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