16. 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.
18. Numerous studies have found that males report higher self-esteem than females, especially for adolescents (Kling, Hyde, Showers, & Buswell, 1999). Typical results show a mean self-esteem score of M = 39.0 with SS = 60.2 for a sample of n =10 male adolescents and a mean of M =35.4 with SS= 69.4 for a sample of n =10 female adolescents.
a. Do the results indicate that self-esteem is significantly higher for males? Use a one-tailed test with = .01.
b. Use the data to make a 95% confidence interval estimate of the mean difference in self-esteem
between male and female adolescents.
c. Write a sentence demonstrating how the results from the hypothesis test and the confidence interval
would appear in a research report.
20. When people learn a new task, their performanceusually improves when they are tested the next day,
but only if they get at least 6 hours of sleep (Stickgold, Whidbee, Schirmer, Patel, & Hobson, 2000). The
following data demonstrate this phenomenon. The participants learned a visual discrimination task on one
day, and then were tested on the task the following day. Half of the participants were allowed to have at
least 6 hours of sleep and the other half were kept awake all night. Is there a significant difference
between the two conditions? Use a two-tailed test with =.05.
Performance Scores
6 Hours of Sleep No Sleep
n =14 n =14
M =72 M =65
SS =932 SS =706
22. Downs and Abwender (2002) evaluated soccer players and swimmers to determine whether the routine blows to the head experienced by soccer players produced long-term neurological deficits. In the study,
neurological tests were administered to mature soccer players and swimmers and the results indicated
significant differences. In a similar study, a researcher obtained the following data.
Swimmers Soccer players
10 7
8 4
7 9
9 3
13 7
7
6
12
a. Are the neurological test scores significantly lower for the soccer players than for the swimmers in the
control group? Use a one-tailed test with= .05.
b. Compute the value of r2 (percentage of variance accounted for) for these data.
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16. a. To determine if there is a significant difference in attitude towards functional foods for males and females, we can conduct an independent samples t-test. First, we calculate the test statistic t, which is given by the formula:
t = (M1 - M2) / √[(SS1/n1) + (SS2/n2)]
where M1 and M2 are the means for females and males respectively, SS1 and SS2 are the sum of squared deviations for females and males respectively, and n1 and n2 are the sample sizes for females and males respectively.
For females:
M1 = 4.69
SS1 = 1.60
n1 = 8
For males:
M2 = 4.43
SS2 = 2.72
n2 = 12
Plugging the values into the formula, we get:
t = (4.69 - 4.43) / √[(1.60/8) + (2.72/12)]
b. To compute the effect size, we can calculate r2 using the formula:
r2 = t2 / (t2 + df)
where t is the test statistic and df is the degrees of freedom, given by (n1 + n2 - 2).
c. In the research report, the results of the hypothesis test would be reported by stating whether there is a significant difference in attitude towards functional foods for males and females at the specified significance level (α=0.05). The effect size would be reported as the percentage of variance accounted for by the gender difference.
18. a. To determine if self-esteem is significantly higher for males, we can conduct an independent samples t-test. Using the given data, we can calculate the test statistic t using the formula mentioned in the previous question.
b. To make a 95% confidence interval estimate of the mean difference in self-esteem between male and female adolescents, we can use the formula:
CI = (M1 - M2) ± t * √[(SS1/n1) + (SS2/n2)]
where M1 and M2 are the means for males and females respectively, SS1 and SS2 are the sum of squared deviations for males and females respectively, and n1 and n2 are the sample sizes for males and females respectively. The t value is determined based on the desired level of confidence (95% in this case) and the degrees of freedom.
c. In the research report, the results of the hypothesis test would be reported by stating whether self-esteem is significantly higher for males at the specified significance level (α=0.01). The confidence interval would be reported to provide an estimate of the mean difference in self-esteem between male and female adolescents with a 95% level of confidence.
20. To determine if there is a significant difference between the two conditions (6 hours of sleep and no sleep) in terms of performance scores, we can conduct an independent samples t-test similar to the previous questions.
a. Calculate the test statistic t using the formula mentioned before.
22. a. To determine if there is a significant difference in neurological test scores between soccer players and swimmers, we can conduct an independent samples t-test similar to the previous questions.
b. Calculate the value of r2 using the formula mentioned before.