Problem Set 1
Whenever appropriate, specify the null hypothesis.
You must show your calculations, by, for example, inserting a pic into your Word document.
Problems 3, 4, 6, 7, and 8must be done by hand and on the computer using statistical software (SPSS or JASP). Copy and insert the results into your problem set at the appropriate place.
Assume that the alpha-level is .05 unless the problem states otherwise.
1. You work for a market research firm. One month's sample of 75 stores shows that mean sales of a small appliance are at 52 units with a standard deviation of 13 units. During the same month last year, a sample of 53 different stores had mean sales of 49 units with a standard deviation of 11 units. The manufacturer is happy because sales went up by 6%. As the market researcher, construct a 95% confidence interval for the "real" difference in the means between now and a year ago. What do you tell the manufacturer? What is the effect size (Cohen's d)?
a) 95% Confidence Interval:
b) What do you tell the manufacturer?
c) What is the effect size (Cohen's d)?
2. 74% of the first-year class at the University of California at Berkeley scored over 500 points on the verbal section of the SAT (a standard test for applicants to U.S. universities). If the verbal SAT scores for the entire class have an SD of 80 points and follow the normal curve, what is the average?
3. Suppose that we sampled children from Somnolent School and Pushup Prep and measured the number of sit-ups that the children at the two schools could do in one minute. Does physical fitness differ across the two schools? Form a 99% confidence interval for the difference between means.
SS: 0 0 1 0 2 3
PP: 5 6 9 8
a) Stated Conclusion (i.e., Does physical fitness differ across the two schools?):
b) 99% Confidence Interval:
c) Statistical Software Output:
4. In a large corporation, the mean salary for all males with 3 to 5 years of experience was $68,000. Salaries (expressed in thousands) for a random sample of 5 women also having 3 to 5 years of experience were:
64 67 69 61 59
Is there evidence of different salary levels for males and females? What is the 95% confidence interval for the mean salary of women with 3-5 years of experience? What it the effect size?
a) Stated Conclusion:
b) 95% Confidence Interval:
c) Effect Size:
d) Statistical Software Output:
5. A study compared the felt intensity of unrequited love among three groups:
(Group 1) 50 participants who were currently experiencing unrequited love; mean experienced intensity = 3.5, standard deviation = 2.28,
(Group 2) 49 participants who had previously experienced unrequited love and described their experience retrospectively; M = 3.2, SD = 2.41, and
(Group 3) 51 participants who had never experienced unrequited love but described how they thought they would feel if they were to experience it; M = 3.8, SD = 2.19.Do these groups differ in felt intensity? Conduct an ANOVA and make a conclusion. Calculate two different measures of effect size.
a) Stated Conclusion:
b) First Effect Size:
c) Second Effect Size:
6. Art Student wants to know if the flower paintings of Georgia O'Keeffe have a greater impact upon the viewer when they are seen in large size rather than in miniature. Since both large and small books of her flower paintings are available, he sets up a matched-pairs design in which each painting is shown to one person in miniature size and to another in a large size. The 10 viewers are randomly assigned to one of the five paintings in either a large or small size. Each viewer is then asked to rate the painting on how much emotional impact it has upon him or her on a 6-point scale ranging from 0 (none) to 5 (overwhelming). Here are the data:
Painting miniature large size
lily 0 2
morning glory 1 2
pansy 2 4
rose 3 4
peony 0 1
Does size matter? Answer the question using a t-test and an ANOVA.
Calculate a 95% confidence interval for the mean difference in emotional impact between the larger-sized and the smaller-sized paintings.
Calculate the effect size in three different ways.
a) Stated Conclusion (t-test):
b) Sated Conclusion (ANOVA):
c) 95% Confidence Interval:
e) First Effect Size:
e) Second Effect Size:
f) Third Effect Size:
g) Statistical Software Output (t-test):
h) Statistical Software Output (ANOVA):
7. Now Art decides to run the same experiment using a within-subjects design. He tests 6 participants. Each one rates 10 images, which are presented in random order. For each participant, half of the images are in large size, the other half are in miniature. Whether each image is presented in large size or miniature is counterbalanced across participants. For each participant, two average ratings are calculated: one for large size images, the other for miniatures.
Participant large size miniature
A 3.8 3.7
B 4.2 3.3
C 2.7 2.2
D 3.5 3.0
E 2.9 0.8
F 4.3 3.8
Does size matter? Answer the question using a t-test.
Calculate a 95% confidence interval for the mean difference in emotional impact between the larger-sized and the smaller-sized paintings.
Calculate the effect size.
a) Stated Conclusion:
b) 95% Confidence Interval:
c) Effect size:
d) Statistical Software Output:
8. A researcher is interested in the self-esteem levels of teachers of three different subjects, so she administers a scale that measures self-esteem to 10 teachers. Higher scores indicate more self-esteem. The scores for four English teachers were 2, 2, 3, and 5. For three math teachers, self-esteem scores were 6, 4, and 5. For three social studies teachers, scores were 9, 10, and 13. Conduct an ANOVA. Calculate two measures of effect size.
a) Stated Conclusion:
b) First Effect Size:
c) Second Effect Size:
d) Statistical Software Output: