Functional foods are those containing nutritional

supplements in addition to natural nutrients. Examples
include orange juice with calcium and eggs with
omega-3. Kolodinsky, et al. (2008) examined attitudes
toward functional foods for college students. For
American students, the results indicated that females
had a more positive attitude toward functional foods
and were more likely to purchase them compared to
males. In a similar study, a researcher asked students
to rate their general attitude toward functional foods
on a 7-point scale (higher score is more positive). The
results are as follows:
Females Male
n � 8 n � 12
M � 4.69 M � 4.43
SS � 1.60 SS � 2.72
a. Do the data indicate a significant difference in
attitude for males and females? Use a two-tailed
test with � � .05.
b. Compute r2, the amount of variance accounted for
by the gender difference, to measure effect size.
c. Write a sentence demonstrating how the results of
the hypothesis test and the measure of effect size
would appear in a research report.

a. Using a two-tailed test with α = .05, the data do not indicate a significant difference in attitude for males and females (t(18) = .38, p > .05).

b. To compute r2, we need to divide the difference in means by the average of the two sample variances. In this case, r2 = (.26 - .22) / [(1.60^2 + 2.72^2) / 2] = .008.

c. The results of the hypothesis test indicate that there is no significant difference in attitude between males and females towards functional foods. Additionally, the effect size (r2 = .008) suggests that the gender difference accounts for a very small amount of variance in attitudes towards functional foods.

a. To determine if there is a significant difference in attitude between males and females towards functional foods, we can conduct a two-tailed t-test with a significance level of 0.05.

First, we need to calculate the degrees of freedom (df) using the formula:
df = n1 + n2 - 2
where n1 is the number of observations for females (8 in this case) and n2 is the number of observations for males (12 in this case).
df = 8 + 12 - 2 = 18

Next, we calculate the pooled standard deviation (Sp) using the formula:
Sp = sqrt(((n1 - 1) * S1^2 + (n2 - 1) * S2^2) / df)
where S1 and S2 are the sample standard deviations for females and males, respectively.
Sp = sqrt(((8 - 1) * 1.60^2 + (12 - 1) * 2.72^2) / 18) = 2.183

Then, we calculate the t-value using the formula:
t = (M1 - M2) / (Sp * sqrt(1/n1 + 1/n2))
where M1 and M2 are the sample means for females and males, respectively.
t = (4.69 - 4.43) / (2.183 * sqrt(1/8 + 1/12)) ≈ 0.26

Finally, we compare the calculated t-value to the critical t-value from the t-distribution table. Since this is a two-tailed test, we divide the significance level (0.05) by 2 to get the critical value. Looking up the value in the t-distribution table with 18 degrees of freedom and a significance level of 0.025, we find the critical t-value to be approximately 2.101.

Since the calculated t-value (0.26) is less than the critical t-value (2.101), we fail to reject the null hypothesis. Therefore, the data does not indicate a significant difference in attitude for males and females towards functional foods.

b. To compute r^2, the amount of variance accounted for by the gender difference, we can use the formula:
r^2 = t^2 / (t^2 + df)
where t is the calculated t-value and df is the degrees of freedom.
r^2 = 0.26^2 / (0.26^2 + 18) ≈ 0.017

The computed r^2 value is approximately 0.017, indicating that the gender difference explains approximately 1.7% of the variance in attitudes towards functional foods.

c. In the research report, the results of the hypothesis test and the measure of effect size would be presented as follows:
"The hypothesis test comparing the attitudes of males and females towards functional foods did not yield a significant difference (t(18) = 0.26, p > 0.05, two-tailed). Furthermore, the effect size, as measured by r^2, indicated that the gender difference accounted for approximately 1.7% of the variance in attitudes towards functional foods."