Homework Assignment Week 6 Name
PSY/CJ 315
1. The following sample of n=6 scores was obtained from a population with unknown parameters. Scores: 5, 5, 3, 4, 6, 7
a. Compute the sample mean and standard deviation. (Note that these are descriptive values that summarize the sample data.)
Sample Mean: M= ΣX / n
M = 5+5+3+4+6+7 / 6
M = 30 / 6
M = 5
Sample Standard Deviation:
s = √ Σ(X-M)2 / n - 1
s = √ (5-5)2 +(5-5)2 + (3-5)2 + (4-5)2 + (6-5)2 + (7-5)2 / 6 -1
s = √ 0 + 0 + 4 + 1 + 1 + 4 / 6 - 1
s = √ 10 / 5
s = 1.41
Population Standard Deviation:
σ = √ Σ(X-M)2 / n
σ = √ (5-5)2 +(5-5)2 + (3-5)2 + (4-5)2 + (6-5)2 + (7-5)2 / 6
σ = √ 0 + 0 + 4 + 1 + 1 + 4 / 6
σ = √ 0 + 0 + 4 + 1 + 1 + 4 / 6
σ = √ 10 / 6
σ = 1.29
b. Compute the estimated standard error for M. (Note that this is an inferential value that describes how accurately the sample mean represents the unknown population mean.)
2. To evaluate the effect of a treatment, a sample of n=8 is obtained from a population with a mean of µ=40, and the treatment is administered to the individuals in the sample. After treatment, the sample mean is found to be M=35.
a. If the sample variance is s2=32, are the data sufficient to conclude that the treatment has a significant effect using a two-tailed test with α=.05?
b. If the sample variance is s2=72, are the data sufficient to conclude that the treatment has a significant effect using a two-tailed test with α=.05?
3. Many animals, including humans, tend to avoid direct eye contact and even patterns that look like eyes. Some insects, including moths, have evolved eye-spot patterns on their wings to help ward off predators. Scaife (1976) reports a study examining how eye-spot patterns affect the behavior of birds. In the study, the birds were tested in a box with two chambers and were free to move from one chamber to another. In one chamber, two large eye-spots were painted on one wall. The other chamber had plain walls. The researcher recorded the amount of time each bird spent in the plain chamber during a 60-minute session. Suppose the study produced a mean of M=37 minutes in the plain chamber with SS=288 for a sample of n=9 birds. (Note: If the eye spots have no effect, then the birds should spend an average of µ=30 minutes in each chamber.)
a. Is this sample sufficient to conclude that the eye-spots have a significant influence on the birds' behavior? Use a one-tailed test with α=.05.
b. Compute the estimated Cohen's d to measure the size of the treatment effect.
c. Construct the 90% confidence interval to estimate the mean amount of time spent on the plain side for the population of birds.
4. A random sample of n=16 scores is obtained from a population with a mean of µ=45. After a treatment is administered to the individuals in the sample, the sample mean is found to be M=49.2.
a. Assuming that the sample standard deviation is s=8, compute r2 and the estimated Cohen's d to measure the size of the treatment effect.
b. Assuming the sample standard deviation is s=20, compute r2 and the estimated Cohen's d to measure the size of the treatment effect.
5. A researcher prepared an example of a vertical-horizontal illusion. Although the two lines are exactly the same, the vertical line appears to be much longer. To examine the strength of this illusion, the researcher prepared the example in which both lines were exactly 10 inches long. The example was shown to individual participants who were told that the horizontal line was 10 inches long and then were asked to estimate the length of the vertical line. For a sample of n=25 participants, the average estimate was M=12.2 inches with a standard deviation of s=1.00.
a. Use a one-tailed hypothesis test with α=.01 to demonstrate that the individuals in the sample significantly overestimated the true length of the line (Note: Accurate estimation would produce a mean of µ=10 inches.)
b. Calculate the estimated d and r2, the percentage of variance accounted for, to measure the size of this effect
c. Construct a 95% confidence interval for the population mean estimated length of the vertical line.
6. A psychologist has prepared an "Optimism Test" that is administered yearly to graduating college seniors. The test measures how each graduating class feels about its future - the higher the score, the more optimistic the class. Last year's class had a mean score of µ=17. A sample of n=9 seniors from this year's class was selected and tested. The scores for these seniors was 9, 15, 13, 16, 9, 10, 17, 11, and 8, which produced a sample mean of M=12 with SS=100.
On the basis of this sample, can the psychologist conclude that this year's class has a different level of optimism than last year's class? Use a two-tailed test with α=.05.
7. The librarian at the local elementary school claims that, on average, the books in the library are more than 20 years old. To test this claim, a student takes a sample of n=30 books and records the publication date for each. The sample produces an average age of M=23.8 years with a variance of s2=67.5. Use this sample to conduct a one-tail test with α=.05 to determine whether the average age of the library books is significantly greater than 20 years (µ>20).
8. Weinstein, McDermott, and Roediger (2010) report that students who were given questions to be answered while studying new material had better scores when tested on the material compared to students who were simply given an opportunity to reread the material. In a similar study, an instructor in a large psychology class gave one group of students, questions to be answered while studying for the final exam. The overall average for the exam was µ=73.4, but the n=16 students who answered questions had a mean of M=78.3 with a standard deviation of s=8.4. For this study, did answering questions while studying produce significantly higher exam scores? Use a one-tail test with α=.05.
9. Ackerman and Goldsmith (2011) found that students who studied text from printed hardcopy had better scores than students who studied from text presented on a screen. In a related study, a professor noticed that several students in a large class had purchased the e-book version of the course textbook. For the final exam, the overall average for the entire class was µ=81.7, but the n=9 students who used e-books had a mean of M=77.2 with a standard deviation of s=5.7.
a. Is the sample sufficient to conclude that scores for students using e-books were significantly different from scores for the regular class? Use a two-tailed test with α=.01.
b. Construct the 95% confidence interval to estimate the mean exam score if the entire population used e-books.
10. Oishi and Shigehiro (2010) report that people who move from home to home frequently as children tend to have lower than average levels of well-being as adults. To further examine this relationship, a psychologist obtains a sample of n=12 young adults who each experienced 5 or more different homes before they were 16 years old. These participants were given a standardized well-being questionnaire for which the general population has an average score of µ=35. The well-being scores for this sample are as follows: 33, 32, 36, 30, 37, 35, 28, 28, 31, 33, 27, 34.
a. On the basis of this sample, is well-being for frequent movers significantly different from well-being in the general population? Use a two-tailed test with α=.01.
b. Compute the estimated Cohen's d to measure the size of the difference.
Extra Credit (+1)
a. Write a sentence demonstrating how the results from the hypothesis test and the confidence interval from problem #9 would appear in a research report.
b. Write a sentence showing how the outcome of the hypothesis test and the measure of effect size from problem #10 would appear in a research report.