Question

Prior to eating breakfast, 25 participants were randomly assigned to eat a large meal, 25 to eat a small meal, and 25 to eat nothing. Immediately following the meal, all participants took a memory test. The means and estimated population variances for the three groups on the memory test were: Large: M = 2.1, S2 = 1.0; Small: M = 2.5, S2 = 1.2; Nothing: M = 2.9, S2 = 0.8. Using the .05 significance level, does amount of breakfast eaten affect memory? Perform a complete hypothesis test.

Answer 1

Answer)

Null hypothesis Ho : u1 = u2 = u3 (that is meal doesn't affect memory)

Alternate hypothesis Ha : atleast 1 is different (that is meal affects memory)

Here we need to use ANOVA,

First we need to find weighted mean,

= (2.1 + 2.5 + 2.9)/3

= 2.5

f1 = sum of squares between groups = ((2.5 - 2.1)^2 + (2.5 - 2.5)^2 + (2.9 - 2.5)^2)* 25 = 8

MS between = (sum of square between group)/df

Df = number of groups - 1 = 3 - 1 = 2

So, Ms b/w = 8/2 = 4

Ms within = (SS With in )/df

Df within = total n - 3 = (25+25+25 - 3) = 72

SS = (N1-1)*S1^2 + (N2-1)*S2^2 + (N3-1)*S2^2 = 72

Ms with in = 72/72 = 1

Test statistics F = ms b/w/ms within = 4/1 = 4.

For alpha = 0.05 and df (2, 72),

F critical value is 3.124

Rejection region is greater than 3.124.

Reject Ho if test statistic statistics is greater than 3.124.

Since 4 > 3.124.

Reject Ho.

We have enough evidence to conclude that meal affects the memory.