Problem 2
A (hypothetical) experiment is conducted on the effect of alcohol on perceptual motor ability. Ten subjects are each tested twice, once after having two drinks and once after having two glasses of water. The two tests were on two different days to give the alcohol a chance to wear off. Half of the subjects were given alcohol first and half were given water first. The scores of the 10 subjects are shown below. The first number for each subject is their per- formance in the "water" condition. Higher scores reflect better performance. Test to see if alcohol had a significant effect. Report the \(\mathrm{t}\) and \(\mathrm{p}\) values. $$ \begin{array}{|c|c|} \hline \text { water } & \text { alcohol } \\ \hline 16 & 13 \\ \hline 15 & 13 \\ \hline 11 & 10 \\ \hline 20 & 18 \\ \hline 19 & 17 \\ \hline 14 & 11 \\ \hline 13 & 10 \\ \hline 15 & 15 \\ \hline 14 & 11 \\ \hline 16 & 16 \\ \hline \end{array} $$
Problem 4
The sampling distribution of a statistic is normally distributed with an estimated standard error of \(12(\mathrm{df}=20)\). (a) What is the probability that you would have gotten a mean of 107 (or more extreme) if the population parameter were \(100 ?\) Is this probability significant at the .05 level (two- tailed)? (b) What is the probability that you would have gotten a mean of 95 or less (one-tailed)? Is this probability significant at the .05 level? You may want to use the t Distribution calculator for this problem.
Problem 7
Below are data showing the results of six subjects on a memory test. The three scores per subject are their scores on three trials \((\mathrm{a}, \mathrm{b},\) and \(\mathrm{c})\) of a memory task. Are the subjects get- ting better each trial? Test the linear effect of trial for the data. $$ \begin{array}{|c|c|c|} \hline a & b & c \\ \hline 4 & 6 & 7 \\ \hline 3 & 7 & 8 \\ \hline 2 & 8 & 5 \\ \hline 1 & 4 & 7 \\ \hline 4 & 6 & 9 \\ \hline 2 & 4 & 2 \\ \hline \end{array} $$ a. Compute \(L\) for each subject using the contrast weights \(-1,0,\) and \(1 .\) That is, compute \((-1)(a)+(0)(b)+(1)(c)\) for each subject. b. Compute a one-sample t-test on this column (with the \(L\) values for each subject) you created.
Problem 10
You have 4 means, and you want to compare each mean to every other mean. (a) How many tests total are you going to compute? (b) What would be the chance of making at least one Type I error if the Type I error for each test was 05 and the tests were independent? (c) Are the tests independent and how does independence/non-independence affect the probability in (b).
Problem 11
In an experiment, participants were divided into 4 groups. There were 20 participants in each group, so the degrees of freedom (error) for this study was \(80-4=76\). Tukey's HSD test was performed on the data. (a) Calculate the \(\mathrm{p}\) value for each pair based on the \(\mathrm{Q}\) value given below. You will want to use the Studentized Range Calculator. (b) Which differences are significant at the .05 level? $$ \begin{array}{|c|c|} \hline {\text { Comparison of Groups }} & \mathrm{Q} \\ \hline \mathrm{A}-\mathrm{B} & 3.4 \\ \hline \mathrm{A}-\mathrm{C} & 3.8 \\ \hline \mathrm{A}-\mathrm{D} & 4.3 \\ \hline \mathrm{B}-\mathrm{C} & 1.7 \\ \hline \mathrm{B}-\mathrm{D} & 3.9 \\ \hline \mathrm{C}-\mathrm{D} & 3.7 \\ \hline \end{array} $$
Problem 12
If you have 5 groups in your study, why shouldn't you just compute a t test of each group mean with each other group mean?
Problem 15
You perform a one-sample t test and calculate a t statistic of 3.0 . The mean of your sample was 1.3 and the standard deviation was \(2.6 .\) How many participants were used in this study?
Problem 17
True/false: If you are making 4 comparisons between means, then based on the Bonferroni correction, you should use an alpha level of .01 for each test.
