Question

Functional foods are those containing nutritional supplements in addition to natural nutrients. For example, orange juice with calcium. A researcher asked students to rate their general attitude towards functional foods on a 7-point scale (higher score is more positive). Females n = 8, M = 4.69, SS = 1.60. Males n = 12, M = 4.43, SS = 1.72. Do the data indicate a significant difference in attitude for males and females? Use a two-tailed test with α = .05

The t-statistic is:

Compute r²

Answer 1

A t-test is used when you're looking at a numerical variable

Null Hypothesis

H0: u1 - u2 = 0, where u1 is the mean of first population and u2 the mean of the second.

As above, the null hypothesis tends to be that there is no difference between the means of the two populations;

Equation

females

N1: 8
df1 = N - 1 = 8 - 1 = 7
M1: 4.69
SS1: 1.60
s21 = SS1/(N - 1) = 1.6/(8-1) = 0.2285

Male

N2: 12
df2 = N - 1 = 12 - 1 = 11
M2: 4.43
SS2: 1.722
s22 = SS2/(N - 1) = 1.72/(12-1) =0.1563

T-value Calculation

s2p = ((df1/(df1 + df2)) * s21) + ((df2/(df2 + df2)) * s22) = ((7/18) *0.2285) + ((11/18) *0.1563) = 0.1843

s2M1 = s2p/N1 = 0.1843/8 = 0.02303
s2M2 = s2p/N2 = 0.1843/12 = 0.01535

t = (M1 - M2)/√(s2M1 + s2M2) = /√119.86 = 0.26/0.1959=1.3268

The t-value is -0.8612. The p-value is in excel as =T.DIST.2T(1.3268,18)=0.2011. The result is not significant at p < .05.

Compute r2, if you mean the R², then we can nor calculate it, becouse for regression we need the equal number of sample.

if you have any difficulty yo understand then comment

Thanks