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Hypothesis Testing & Cohen's d

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Problem Set 1: Chapter 10: problems 2, 14, 22, 24; Chapter 11, problems 2, 4, 12, 20

Chapter 10

2. Describe what is measured by the estimated standard error in the bottom of the independent measures t test.
14. Do you view a chocolate bar as delicious or as fattening...?

Males Females
n = 6 n = 9
M = 31 M = 45
SS = 490 SS = 680
a. Based on these results, is there a significant difference between the attitudes for males and for females? Use a two-tailed test with ? = .05.
b. Compute r2, the percentage of variance accounted for by the gender differences to measure effect size for this study.
22. Steven Schmidt (1994)...Use a two-tailed test with ? = .05

Humorous Sentences Nonhumorous Sentences

4 5 2 4 6 3 5 3
6 7 6 6 3 4 2 6
2 5 4 3 4 3 4 4
3 3 5 3 5 2 6 4
Do the results indicate a significant difference in the recall of humorous versus non-humorous sentences? Use a two-tailed test with alpha = .05.
24. A researcher conducts an independent measures research study and obtains t = 2.070 with df = 28.
a. How many individuals participated in the entire study?
b. Using a two-tailed test with a = .05, is there a significant difference between the two treatment conditions.
c. Compute r2 to measure the percentage of variance accounted for by the treatment effect.
Chapter 11
2. Participants enter a research study with unique characteristics that produce different scores from one person to another. For an independent-measures study, these individual differences can cause problems. Briefly explain how these problems are eliminated or reduced with a repeated-measures study.
4. A researcher conducts an experiment comparing two treatment conditions and obtains data with 10 scores for each treatment condition.
a. If the researcher used an independent-measures design, how many subjects participated in the experiment?
b. If the researcher used a repeated-measures design, how many subjects participated in the experiment?
c. If the researcher used a match-subjects design, how many subjects participated in the experiment?
12. The stimulant Ritalin has been shown to increase attention span and improve academic performance in children with ADHD...n = 25, MD = 6.8, s = 5.5.
a. Is this result sufficient to conclude that Ritalin has a significant effect on attention span? Use a two-tailed test with ? = .01.
b. Compute r2 and an estimated Cohen's d to measure the size of the effect.
20. A researcher uses a matched samples design to investigate whether single people who own pets are generally happier than singles without pets. Test with ? = .05, two-tailed.

Matched Pair Participants from US Pet Owner
A 10 15
B 9 9
C 11 10
D 11 19
E 5 17
F 9 15

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Solution Summary

The solution provides step by step method for the calculation of testing of hypothesis. Formula for the calculation and Interpretations of the results are also included. Interactive excel sheet is included. The user can edit the inputs and obtain the complete results for a new set of data.

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Hypothesis Testing, Power of Hypothesis Testing & Cohen's d

2. The value of the z-score in a hypothesis test is influenced by a variety of factors. Assuming that all other variables are held constant, explain how the value of z is influenced by each of the following.

a. Increasing the difference between the sample mean and the original population mean.

b. Increasing the population standard deviation.

c. Increasing the number of scores of the sample.

4. If the alpha level is changed from ? = .05 to ? = .01.

a. What happens to the boundaries for the critical region?

b. What happens to the probability of a Type 1 error?

6. A researcher is investigating the effectiveness of a new study skills training program for elementary school children. A sample of n = 25 third grade children is selected to participate in the program and each child is given a standardized achievement test at the end the year. For the regular population of third grade children, scores on the test form a normal distribution with a mean of µ= 150 and standard deviation of Ï? = 25. The mean for the sample is M = 158.

a. Indenify the independent and the dependent variables for this study.

b. Assuming a two-tailed test, state the null hypothesis in a sentence that includes the independent variable and the dependent variable.

c. Using symbols, state the hypothesis (Ho and H1) for the two-tailed test.

d. Sketch the appropriate distribution, and locate the critical region for ? = .05

e. Calculate the test statistic (z-score) for the sample.

f. What decision should be made about the null hypothesis, and what decision should be about the effect of the program?

10. State College is evaluating a new English composition course for freshmen. A random sample of n = 25 freshmen. A random sample of n =25 freshmen is obtained and the students are placed in the course during their first semester. One year later, writing samples are graded using a standardized evaluation technique. The average score for the sample is M = 76. For the general population of college students, writing scores form a normal distribution with a mean of µ =70.

a. If the writing scores of the population have a standard deviation of Ï? =20, does the sample provide enough evidence to conclude that the new composition course has a significant effect? Assume a two-tailed test with ? = .05.

b. If the population standard deviation is Ï? = 10, is the sample sufficient to demonstrate a significant effect. Again, assume a two-tailed test with ? = .05.

c. Briefly, explain why reached different conclusion for part (a) and part (b).

18. A sample of n = 16 individuals is selected from a normal population with the mean of µ = 48 and the standard deviation of Ï? = 12. After receiving a treatment, the sample mean is found to be M = 52.

a. Compute Cohen's d to evaluate the size of the treatment plan.

b. If the sample size were n = 36, what value would be obtained for Cohen's d? How does sample size influence the measure of effect size?

c. If population standard deviation were Ï? =24 what value would be obtained for Cohen's d? How does the standard deviation influence the measure of effect size?

d. If the sample mean were M =56, what value would be obtained for Cohen's d? How does the size of the mean difference influence the measure of effect size?

22. Explain how the power of a hypothesis test is influenced by each of the following. Assume that all other factors are held constant.

a. Increasing the alpha level from .0.1 to .05.

b. Changing from a one-tailed test to a two-tailed test.

24. A researcher is evaluating the influence of a treatment using a sample selected from a normally distributed population with a mean of µ =80 and a standard deviation of Ï? = 20. He researcher expects a 12- point treatment effect and plans to use a two-tailed hypothesis test with ? = .05.

a. Compute the power of test if the researcher uses a sample of n =16 individuals.

b. Compute the power of the test if the researcher uses a sample of n = 25 individuals.

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