Reference no: EM132536091

EDS 504 Educational Statistics - Middle East Technical University

Part 1:

Problem 1:

A sample of n = 16 individuals is selected from a normal population with μ = 65 and σ = 6. A treatment is administered to the individuals in the sample, and after the treatment, the sample mean is found to be M = 67.

a. On the basis of the sample data, can you conclude that the treatment has a significant effect?

Use a two-tailed test with α = .05.

b. Suppose that the sample consisted of n = 64 individuals and produced a mean of M = 67.

Repeat the hypothesis test at the .05 level of significance.

c. Compare the results from part a and part b. How does the sample size influence the outcome of a hypothesis test?

Problem 2:

A researcher is testing the hypothesis that consuming a sports drink during exercise will improve endurance. A sample of n= 50 male college students is obtained and each students is given a series of three endurance tasks and asked to consume 4 ounces of the drink during each break between tasks. The overall endurance score for this sample is M=54. For the general population, without any sports drink, the scores for this task average μ= 50 with a standard deviation of 12. Can the researcher conclude that consuming sports drink during exercise has a significant effect on endurance scores?

a. Do the data from this sample provide evidence for a significant difference in REM activity during exams? Set α = .05, and perform a two-tailed hypothesis test.

b. Repeat the hypothesis test using α = .01.

c. Explain why the change in α from .05 to .01 (part a versus part b) caused a change in the conclusion.

Problem 3:

On a standardized anagram task (anagrams are sets of scrambled letters that must be arranged to form words), people successfully complete an average of μ =34 anagrams with σ = 8. This distribution is normal. A researcher would like to demonstrate that the arousal from anxiety is distracting and will decrease task performance. A sample of n = 24 anxiety-ridden people is tested on the task. The average number of anagrams solved is M =30.

a. Do the anxiety-ridden participants show a decrease in task performance? Test with alpha set at .01 for one tail.

b. If a two-tailed test with α = .01 was used, what conclusion should be drawn?

Part 2:

Problem 1. Several years ago, a survey in a school district revealed that the average age at which students first tried an alcoholic drink was μ = 16 years. To determine whether anything has changed, a random sample of students was asked questions about alcohol use. The age at which drinking behavior first began was reported by members of the sample as follows: 9, 15, 10, 11, 10. Has there been a change in the mean age at which drinking began?

Test at the .05 level of significance (two-tail). Here is what we want you to do for this question:

1. State your hypotheses (both null and alternative) verbally and in statistical terms,

2. Set the criteria for a decision (locate your critical values),

3. Perform a single-sample t-test by hand calculations.

4. Indicate your statistical conclusion; that is, reject or fail to reject H0.

5. Calculate effect size (both Cohen's d and eta-squared) by hand and interpret them, if required
6. Report your findings (including descriptive statistics) in APA format.

Problem 2. On a standardized spatial skills task, normative data reveal that people typically get μ = 14 correct solutions. A psychologist tests n = 6 individuals who have brain injuries in the right cerebral hemisphere. For the following data, determine whether or not right-hemisphere damage results in significant change in performance on the spatial skills task. Test with alpha set at .05 with two-tail. The data are as follows:
14, 11, 10, 12, 13, 12,

Here is what we want you to do for this question:

1. State your hypotheses (both null and alternative) verbally and in statistical terms,

2. Set the criteria for decision (i.e. locate your critical values),

3. List assumptions to be satisfied (Just list their names, no need to run any analyses)

4. Using SPSS, perform a single-sample t-test. Attach relevant SPSS output to your assignment. Attach relevant SPSS output to your assignment. SPSS output is not expected to be in APA format. Please note that you are not asked to do hand calculations.

5. Indicate your statistical decision.

6. Calculate effect size (both Cohen's d and eta-squared) by hand and interpret them, if required.

7. Report your findings (including descriptive statistics) in APA format.