F Test and ANOVA Homework Name: 1. An existing drug has a small ideal therapeutic range. A substitute generic version claimed to have a similar narrow range. Use Excel to conduct an \( F \) test at \( \alpha=.05 \) to determine to determine if the two drugs have the same or a different variance. Write steps \( 1-5 \) of the hypothesis test on your excel printout. Do NOT work a \( H_{0}: \mu_{1}-\mu_{2}=0 \) hypothesis test or confidence interval. \[ \begin{array}{lll} n=25, & \bar{x}=101.5 & s=1.3 \\ n=21, & \bar{x}=98.6 & s=1.8 \end{array} \] 2. Four final grade test samples were taken from a high school course taught by four different professors. Use Excel to conduct an \( F \) test at \( \alpha=.05 \) to determine if the means of all these samples are from the same distribution. You may write hypothesis steps \( 1-5 \) on your printout. \begin{tabular}{llll} Y1i & Y2i & Y3i & Y4i \\ 86 & 90 & 74 & 81 \\ 79 & 76 & 68 & 69 \\ 81 & 88 & 73 & 71 \\ 70 & 82 & 75 & 67 \\ 84 & 89 & 81 & 81 \\ & & 86 & \\ & & 70 & \end{tabular}
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5. Hypothesis testing with ANOVA Opinions about whether caffeine enhances test performance differ. You design a study to test the impact of drinks with different caffeine contents on students' test-taking abilities. You choose 21 students at random from your introductory psychology course to participate in your study. You randomly assign each student to one of three drinks each with a different caffeine concentration, such that there are seven students assigned to each drink You then give each of them plain capsule containing the precise quantity of caffeine that would be consumed in their designated drink and have them take an arithmetic test 15 minutes later. The students receive the following arithmetic test scores: Water Black Tea Coffee Caffeine Content (mg/oz) 0 5.9 13.4 78 85 92 EX2 = 144,239 88 89 87 G = 1,733 72 82 80 N = 21 72 75 89 k = 3 64 88 96 81 76 83 82 82 92 T1 = 537 T2 = 577 T3 = 619 SS1 = 381.43 SS2 = 177.71 SS3 = 185.71 n1 = 7 n2 = 7 n3 = 7 M1 = 76.7143 M2 = 82.4286 M3 = 88.4286
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An experimenter was interested in investigating the effects of two stimulant drugs (labeled A and B). She divided 20 rats equally into 5 groups (placebo, drug A low dose, drug A high dose, drug B low dose, drug B high dose). Each rat's activity level (higher score is more active) was recorded 20 minutes after injection of the drug. The following table summarizes the results: Treatment | Sample size | Mean | STD Placebo | 4 | 14.00 | 2.828 Low A | 4 | 15.25 | 3.500 High A | 4 | 18.25 | 3.500 Low B | 4 | 16.75 | 2.550 High B | 4 | 22.50 | 3.317 Construct the ANOVA table. Provide the approximate p-value using the F-table. Make sure to show your work. Test the hypotheses of interest using α=0.05. Use Tukey's method for paired comparisons to rank the 5 treatments.
PLEASE SHOW IN EXCEL You need to decide if two teachers teach the same or differently. You have randomly assigned students to the different teachers. Then, the students take a standard exam at the end of the class. The scores for the teachers are: Teacher 1 Teacher 2 35 52 51 87 66 76 42 62 37 81 46 71 60 55 55 67 53 Did one teacher do better or worse than another teacher? State your hypothesis and your null hypothesis: Decide which t-test you will use (Dependent, Independent – equal variance, Independent – unequal variance): Test your null hypothesis at the .05 level (decide if this is one-tailed or two-tailed). Which tailed test did you use and what is your observed t value? What is the critical value for this test? Do you accept or reject your null hypothesis? State your conclusion:
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