It is important for me to see all formulas and work on this one. step by step fo
ID: 3204442 • Letter: I
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It is important for me to see all formulas and work on this one. step by step for each part. Last help sent answers and some work, but I really need it broken down. I understand it but want to make sure I am configuring the correct items. Thank you so much.
12) Marshall is superstitious and suspects that people who take the GRE while wearing the same dirty socks that they wore when they got their best score on a practice test will do better than people who do not wear these “lucky” socks. In order to test that hypothesis among college students, he made 20 students wear their “lucky” socks and 20 not wear their lucky “socks” while taking the GRE test. Although he was convinced that people who wore their “lucky” socks would score higher than people who didn’t, he wanted to be able to test the possibility that they could score lower. Their scores are as follows:
“Lucky” Non-“Lucky”
Sock wearers Sock Wearers
108 105
107 107
112 110
113 109
105 105
100 114
120 98
*For this problem, you will be conducting a t test for independent means. See pages 284-286 for an example of conducting this type of analysis and model your response after that problem.
a) Step 1: What are the two populations? Restate the question as a research hypothesis and a null hypothesis about the populations. Is your research hypothesis directional or non-directional?
b) Step 2: Determine the characteristics of the comparison distribution. In other words, what are the sample means, dfs, the variance of each distribution of means, the variance for the distribution of the differences between means, and the standard deviation of the distribution of the differences of the means? Also, calculate df, and the variance and standard deviations of the distribution of means. Show formulas and all work.
c) Step 3: What is the critical value for this test at alpha = .05 (i.e., significance level of 5%)?
d) Step 4: Determine your samples score on the comparison distribution. That is, calculate the t-test. SHOW ALL WORK and formulas.
e) Step 5: Decide whether to reject the null hypothesis. State in words the results of your study (using an alpha of .05)?
Explanation / Answer
a) The two populations in this case are college students wearing lucky socks and another population waering non lucky socks.
Null hypothesis : there is no difference in average GRE scores between college students wearing lucky socks versus students not wearing lucky socks.
b)
Test for Equal Variances: Lucky, NonLucky
95% Bonferroni confidence intervals for standard deviations
N Lower StDev Upper
Lucky 7 3.90276 6.42169 16.1538
NonLucky 7 3.04740 5.01427 12.6134
F-Test (normal distribution)
Test statistic = 1.64, p-value = 0.563
Levene's Test (any continuous distribution)
Test statistic = 0.33, p-value = 0.575
The variance are equal.
Two-Sample T-Test and CI: Lucky, NonLucky
Two-sample T for Lucky vs NonLucky
N Mean StDev SE Mean
Lucky 7 109.29 6.42 2.4
NonLucky 7 106.86 5.01 1.9
Difference = mu (Lucky) - mu (NonLucky)
Estimate for difference: 2.42857
95% CI for difference: (-4.28097, 9.13811)
T-Test of difference = 0 (vs not =): T-Value = 0.79 P-Value = 0.446 DF = 12
Both use Pooled StDev = 5.7611
There is no difference in the average score between students wearing lucky socks versus not weraing socks.
c) critical value =0.446
d)T value = 0.79
e). Fail to reject Ho.
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