Question

2. E Bergman et al conducted, a study to determine, among other things, the impact that scheduling recess before or after lunch period has on wasted food for students in grades 3 through 5. Results were published in the article "The relationship of meal and recess schedules to plate waste in elementary school." Journal of Child Nutrition and Management. Summary statistics of the amount of food wasted in grams are given below.

Lunch Before recess, Lunch after recess

Mean 223.1, 156.6

Standard deviation 122.9, 108.1

n 889, 1119

a. At the 1% significance level, do the data provide sufficient evidence to conclude that, in grades three through five, the mean amount of food wasted for lunches before recess exceeds that for lunches after recess?

b. How much more food is wasted when lunch is before recess? *Think confidence interval....) Write a sentence interpreting the number(s) you provide.

Answer 1

The sample means are , . The sample standard deviations are

and sample sizes are

The estimated mean difference is

The sample standard deviation of the differences is

We have to test (Right tailed Z-test)

The P-value of the test is

The rejection region is . Since

, there is statistically significant difference between the means at  .

Reject null hypothesis. Coclusion: the mean amount of food wasted for lunches before recess exceeds that for lunches after recess

b) An average of more food is wasted when lunch is before recess.