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The School Nutrition Association wants to study the average number of calories in home-packed lunches for...

The School Nutrition Association wants to study the average number of calories in home-packed lunches for elementary students. Specifically, they want to know if home-packed lunches have significantly more calories than the recommended 600 calories needed for daily energy and health. In a sample of 25 home-packed lunches, the average number of calories was 615 calories with a standard deviation of 30 calories. Use the appropriate analysis to determine if the average home-packed lunch is greater than 600 calories.

Identify the null and the alternative hypothesis.

math   Statistics-And-Probability   
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Answer #1

To Test :-

H0 :- µ = 600
H1 :- µ > 600

Test Statistic :-
t = ( X̅ - µ ) / (S / √(n) )
t = ( 615 - 600 ) / ( 30 / √(25) )
t = 2.5

Test Criteria :-
Reject null hypothesis if t > t(α, n-1)
Critical value t(α, n-1) = t(0.05 , 25-1) = 1.711
t > t(α, n-1) = 2.5 > 1.711
Result :- Reject null hypothesis

There is sufficient evidence to support the claim that  the average home-packed lunch is greater than 600 calories.

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