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1.A sample is selected from a population with µ = 80. After a treatment is administered to the individuals, the sample mean is found to be M = 75 and the variance is s2 = 100.
a. If the sample has n = 4 scores, then calculate the estimated standard error and determine whether the sample is sufficient to conclude that the treatment has a significant effect? Use a two-tailed test with alpha = 0.05
b. If the sample has n=25 scores, then calculate the estimate standard error and determine whether the sample is sufficient to conclude that the treatment has a significant effect? Use a two-tailed test with alpha = 0.05
c. Describe how increasing the size of the sample affects he stanard erro and the likelihood of rejecting null hypothesis
2.A researcher is testing the effect of a new cold and flu medication on mental alertness. A sample of n=9 college students is obtained and each student is given the normal dose of the medicine. Thirty minutes later, each students performance is measured on a video game that requires careful attention and quick decision making. The scores for the nine students are as follows: 6,8,10,6,7,13,5,5,3.
a. Assuming that scores for students in the regular population average u=10, are the data sufficient to conclude that the medication has a significant effect on mental performance? Test at the .05 level of significance.
b. Compute r2, the percentage of variance explained by treatment effect.
c. Write a sentence demonstrating how the outcome of the hypothesis test and the measure of effect size would be presented in a research report.
3.A researcher conducts an independent-measures study examining how the brain chemical serotonin is related to aggression. One sample of rats serves as a control group and receives a placebo that does not affect normal levels of serotonin. A second sample of rats receives a drug that lowers brain levels of serotonin. Then the researcher tests the animals by recording the number of aggressive responses each of the rats display. The data are as follows.
Control Low Serotonin
n = 10 n = 15
M = 14 M = 19
SS = 180.5 SS = 130.0
a. Does the drug have a significant effect on aggression? Use an alpha level of .05, two
tails.
4. An educational psychologist studies the effect of frequent testing on retention of class material. In one section of an introductory course, students are given quizzes each week. A second section of the same course receives only two tests during the semester. At the end of the semester, both sections take the same final examination. The summarized scores below frequent quizzesn=20, M=73, two exams- n=20;M=68.
a. If the sample variance is s2=38 and second has s2=42, do the data indicate that testing frequency has siggnificant effect on performance? Use a two tailed test at the .05 level of signifficance. (note because the two samples are the same size, the pooled variance is simply the average of the two sample variances.)
b. If the first sample variance is s2=84 and the second sample has s2=96, to tge data indicate that testing has signifficant effect? Again use a two tailed test with Alpha=.05.
c. Describe how the size of the variance effects the outcome of the hypothesis testing?
5. The following data are from an independent-measures experiment comparing two treatment conditions.
treatment 1 is 4,5,12,10,10,7 and treatment 2 is 19,11,18,10,12,14.
a. Do these data indicate a signifficant difference between the tretment at the 0.5 level of significance?
b.wWrite a sentence demonstrating how the outcome of the hypothesis test and the measure of effect size would appear in a research report.
6. One of the major advantages of a repeated-measures desing is that it removes individulal differences from the variance and therefore reduces the standard error. The follwing two sets of data demonstrate this fact. The 1st set of data represents the original results from a repeated measures study. To create the 2nd set of data we started with the original scores but increased the individual differences by adding 10points to each score for subject B, adding 20 points to each score for subject C and adding 30 points to each score for subject D. Note that this change produces a huge increase in the difference from one subject to another and a huge increase in the variability of the scores within each treatment condition
Set 1. Set 2.
Subject I II Subject I II
A 12 14 A 12 14
B 7 17 B 17 27
C 11 12 C 31 33
D 10 12 D 40 42
M=10 M=14 M=25 M=29
SS14 SS=14 SS=494 SS=414
a. Find the difference scored for each set of data and compute the mean and variance for each sample of difference scores.