Analysis of variance compares the means of a response variable for several groups. ANOVA compares the variation within each group to the variation of the mean of each group. The ratio of these two is the F statistic from an F distribution with.. (number of groups - 1) as the numerator degrees of freedom, &  (number of observations - number of groups) as the denominator degrees of freedom. You intend to conduct an ANOVA with 6 groups in which each group will have the same number of subjects: n=18n=18. (This is referred to as a "balanced" single-factor ANOVA.) What are the degrees of freedom for the numerator? d.f.(treatment) =  What are the degrees of freedom for the denominator? d.f.(error) =

11. Hypothesis Test of Equal Variances. Test the given claim. Use a significance level of a = 0.05 and assume that all populations are normally distributed. Claim: The treatment population and the placebo population have different variances. n = 16, x = 21.33, s = 0.80 n = 41, x = 25.34, s = 0.40 Treatment group : Placebo group :

Researchers at UT Austin noticed that the seagrass beds in Corpus Cristi Bay (CCB) were taller and thicker than those in Lower Laguna Madre (LLM). They compared the sediment ammonium concentration, in the two locations. Following are the summary statistics on sediment ammonium concentration, in micromoles, obtained by the researchers. Equality of variances is not assumed. CCB: X₁ 115.1, s₁= 79.4, n₁ = 51 LLM: X₂ = 24.3, S₂ 10.5, n₂: 19 = a. At the 1% significance level, is there sufficient evidence to conclude that the mean sediment ammonium concentration in CCB exceeds that in LLM? b. Determine a 98% confidence interval for the difference μ1-µ2, between the mean sediment ammonium concentrations in CCB and LLM. Interpret your answer in (a) in words. c. Do the results in (a) and (b) provide the consistent results? Explain.

An experiment was conducted on rodents to determine if the drug Haldol influenced the amount of "rough play." Five groups were included in the experiment. Subsequent behavior in terms of mean "rough play" behaviors was recorded. The output and box plot below, display the mean differences from baseline (i.e., after the drug was administered compared to before drug administration). What are the null and alternative hypotheses of this test? Summary of Roughplay differences Scd. Dev. Haldol dese Mean Freq. -.63158419 13.290618 19 Vehicle | 0.025 mg i 0.05 mg/ 1 0.1 mg/k -12.754389 13.783537 0.2 mg/k I 18 1.1481501 20.447041 5.0499951 16.035879 20 19 -20.S5 16.431064 20 Total -5.6631968 1B.558994 96 Analysis of Variance Frob F (p-value) Source SS df KS F Test- Statistic 8999.32832 4 2249.33203 9.63 0.0000 Between groups Within groups 91 260.682623 23722.1178 Tozal 32721.4461 95 344.436275 chif (4) 4.1710 Prob>chiz = 0.303 = Bartlett's test for equal variances: Roeghpiay diferences -50 Ho: 0…