(25) 1. (a) Assume a one-way anova with five treatments and 7 observations per treatment.Find the degrees of freedom for (i) treatments, (ii) error, and (iii) total.

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(b) Refer to the previous problem. Assume MSE : 9. (i) Give an estimate of thestandard deviation of the sum of the mean for treatment 1 and the mean fortreatment 2. (ii) Give an estimate of the standard deviation of the difference

between the mean for treatment 1 and the mean for treatment 2.

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(c) Consider a two-way anova with factors A and B having 3 and 5 levels respectively.

There are 10 observations per cell. Give the degrees of freedom for each of themain effects, the interaction) error) and total.

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ER'ffi 135(d) The sample variances for the three groups with equal sample sizes in a one-way

anova are 22,20, and 24. What is the value of MSE?

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3 :?7(e) You have calculated a collection of confidence intervals using the Tukey procedure.

If you redo the calculations using the LSD procedure which makes no correctionsfor fact that you are computing several intervals. Will the new intervals be wideror narrower than the T\rkey intervals? trxplain your answer.

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(25) 2. (a) An experiment is run with 4 levels of a quantitative factor and 10 observations ateach level. The researchers believe that a quadratic model may give a good fit tothe data. Give the numerator and denominator degrees of freedom for the F testused to examine the lack of fit.

(b) A one-way anova model is used to analyze data for an experiment with 3 treatmentgroups. A 95% confidence interval is constructed for h - Ltz. Suppose that theunderlying model has unequal variances: o? : I0, 03. : 5, and o.2 : 15. Assumethat the sample sizes in the three groups are equal. Will the true confidencecoefficient for the interval be greater than, equal to, or less that g5%. Explainyoul answer.

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(c) To use the Bonferroni procedure, with an overall error rate of 5To, to conrpareall pairs group means in a one-way anova with 5 groups and 6 observations pergroup, you will use a critical value from the I distribution. Using the text notation,t(A;u), give A and u for this problem

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(d) Consider a two-way anova with factors A (with 4 levels) and B (with 3 levels).Assuming that the class statement lists A before B, give the coefficients for thecontrast that you would use to test lIe : ptt : l.tzs.

(") A friend shows you an anova output for a six-way anova. The degrees of freedomfor total are 231. How many observations were used for this analvsis?

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(25) 3. For this question refer to the output for PROC GLM given as OUTPUT FOR PROB-LEM 3.

(a) Write the anova model for this analysis using the cell means model. (Give ex-plicit numerical values for number of groups being compared and the numbers ofobservations per group.)

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(b)

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The first part of the output gives the resultshypothesis tested, test statistic with degrees ofone sentence describing the conclusion in words.

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of a hypothesis test. State ttrefreedom, the P-value and write

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MgNN OI FFGive a confidence interval for pra- l-r1, using the Ttrkey HSD method that gives95% confidence for intervals involving all pairs of means. Use the output to findthis interval.

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(d) Your answer to part (a) should include a parameter o2. What is the estimate ofthis parameter given in the output?

'JG,7t3(e) Summarize the results of the multiple comparison procedure applied to thcse clata.

Be specific.

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(25) 4. For this question refer to the program and output for PROC GLNI given as OUTPUTFOR PROBLEN4 4.

(a) The population means for this problem are py : 10, l.rtz: 12, lltz: 14, 1144:16,l-tzt :20, Fzz:22, llzt: 24, and F24:26. Does this model have an interaction?Give a resaon for your answer. 6 Z

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t'z3q(b) Examine the program carefully. Does

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this analysis have homogeneous variances? Explain your answer.

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(d) Give the smaliest and largest standard devi or the eight cells in this two-v/ay anova. The program specifies that each ofsize 3 from a normal distribution with mean zerostandard dcviations vary so much?

is based on a sample ofriance 1. Why do these

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(e) Assuming that these data came from an experiment, explain what additionalanalyses you would perform to draw conclusions from these data.

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