Question

In an experiment to determine the effect of nutrition on the attention spans of elementary school students, a group of 45 students is divided into three groups of 15, and randomly assigned to each of three meal plans: no breakfast, light breakfast, and full breakfast. Their attention spans, in minutes, were recorded. Say you want to test the hypothesis that the means of the attention spans are not all the same at a level of significance of 5%.

(a) (3 pts) What are the null and alternative hypotheses?

(b) (4 pts) Suppose that you find MSG=26 and MSE=3.1. Find the F-statistic, and estimate the p-value of your data using the F-table.

(c) (3 pts) Should you accept or reject? Explain.

Answer 1

## Q ) In an experiment to determine the effect of nutrition on the attention spans of elementary school students, a group of 45 students is divided into three groups of 15, and randomly assigned to each of three meal plans: no breakfast, light breakfast, and full breakfast. Their attention spans, in minutes, were recorded. Say you want to test the hypothesis that the means of the attention spans are not all the same at a level of significance of 5%.

## : we have given three groups and each group have 15 observation , for this we can use ANOVA Test

## (a) What are the null and alternative hypotheses?

Answer :

Ho : all means are equal ie μ1 = μ2 = μ3

VS

H1 : not all means are equal ie  μ1 ≠ μ2 ≠ μ3  

## (b) Suppose that you find MSG=26 and MSE=3.1. Find the F-statistic, and estimate the p-value of your data using the F-table.

Answer : F = ( MSG / MSE ) = (26 / 3.1 )

= 8.3870

and p value = 0.000862 ( use table )

## (c) ( Should you accept or reject? Explain.

Answer : Decision : we reject Ho if p value is less than alpha value using p value approach here p value is less than alpha value we reject Ho at given level of significance .

we rejecct Ho

Conclusion : There is sufficient evidence to conclude that not all means are equal that means result is significant at given level of significance.  

that the means of the attention spans are not all the same at a level of significance of 5%.