1. Suppose that the F ratio you have calculated for a one-way ANOVA is 23. Which of the following can you conclude?a. A calculation error has probably been made (F values this high don’t happen in real life) b. The null hypothesis can be rejected at .05c. The group means must have been spread far apartd. There must have been very little within-group variabilitye. The same size must have been large 2. A study compares five groups with 10 observations in each group. An F statistic of 3.75 is reported. What are the degrees of freedom for this F statistic?a. 4 and 45 b. 5 and 10c. 4 and 46 d. 5 and 503. A study compares three population means. Three independent samples with 15 observations each are taken. The SSWithin = 1246 and the SSTotal=1600. What is the value of the F statistic?a. 1.11 b. 3.32c. 4.98 d. 5.974. In a study comparing four groups with six observations in each group, the MSWithin = 487 and the MSBetween= 3456. What proportion of the variance in the dependent variable is explained by the independent variable?a. 0.484 b. 0.516c. 0.587 d. 0.939Use the following to answer questions 5 and 6:A realtor wishes to assess whether a difference exists between home prices in three subdivisions. Independent samples of homes from each of the three subdivisions are obtained and their prices are recorded. The analysis of variance results for comparing these prices are provided below:Source Sums of Squares DF Mean Square FGroups 157.44 2 78.72 4.66Error 253.50 15 16.90 Total 410.94 17 5. How many homes were sampled in total?a. 15 b. 17c. 18 d. 196. What can we say about the p value for this F test?a. p value <0.01 b. 0.1 < p < 0.05c. 0.01 < p < 0.05 d. 0.05 < p < 0.10 7. Which of the following tends to increase the size of the F ratio in a RM ANOVA? a. Larger subject-to-subject differences (averaging across treatment levels)b. Better matching of the scores across treatmentsc. Larger subject by treatment interactiond. Smaller differences between treatment means8. An RM ANOVA on a certain set of data did not attain statistical significance. What advantage would be derived from performing an independent groups ANOVA on the same data? a. A larger alpha level would normally be usedb. The numerator of the F ratio would probably be largerc. The critical F would probably be smallerd. The error term would probably be larger 9. The interaction for a particular two-way ANOVA is statistically significant. This implies that:a. Neither of the main effects is significantb. Both of the main effects are significantc. The lines on the graph of cell means will intersectd. The lines on a graph of cell means will not be parallel10. When there is no interaction among the population means in a two-way design, the numerator of the F ratio for interaction in the data from an experiment expected to be:a. About the same as MSwb. Zeroc. About the same as the sum of the numerators for the two main effectsd. Dependent on the number of cells in the design 11. Supposes that F ratio you have calculated for a one-way ANOVA is .04. Which of the following can you conclude?a. A calculation error has probably been madeb. The null hypothesis can be rejected because F<.05c. There must have been a great deal of within group variabilityd. The null hypothesis cannot be rejectede. No conclusion can be drawn without knowing the degrees of freedom12. How many cells are there and what is the value of df within for the following ANOVA designs? (assume n=6 subjects per cell)a. 2X5 (1pt) b. 6X3 (1pt) c. 4X4 (1pt) Part II (computational):1. The following summary table corresponds to a hypothetical experiment in which subjects must complete a mental task at five levels of difficulty and with three different levels of reward. Much of the table has deliberately been left blank, but all of the missing entries can be found by using the information in the previous sentence and the information in the table:source SS Df MS Fdifficulty 100 ? ? ?reward 150 ? ? ?interaction ? ? 5 ?Within ? 90 ? Total 1190 a. Fill in all the missing blanks in the table b. State the null and alternative hypotheses c. State your conclusions ��
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2. A school psychologist is interested in determining the effectiveness of an antidrug film on the attitudes of eight-grade students. Each students’ antidrug attitude is measured on a scale from 0 to 20 (20 representing the strongest opposition to drug use) at four times: the day before the film; as students are sitting in class waiting for the film to start; immediately after the film; and the next day in class. The data for 5 students appear in the table below:Subject Day before Prior to film After film Day afterA 14 15 18 17B 10 13 19 17C 15 15 18 18D 13 16 20 18E 7 9 15 16𝑋2=4811 a. State the null and alternative hypotheses and perform the appropriate ANOVA on these data to determine if there is a difference in attitude over time at the .01 level. (8pts)b. Present the results in an ANOVA summary table (4 pts)c. Draw the appropriate plot (3 pts) 3. An experiment is performed to compare the average reading scores of second grade children taught using four different methods. Students are randomly assigned to the four groups with 20 students per group. An analysis of variance is to be used to analyze the data. The following is a partially completed ANOVA table. Fill in the remaining details (1 pt per blank – 6 possible points):Source Sum of Squares DF Mean Square FGroups 136.21 Error/Within 675.83 Total a. State the null and alternative hypothesis b. Based on the information, would you reject the null hypothesis at alpha=.05 that all four groups of second grade students will have the same average reading scores? what is the critical value of F? c. How much of the variability in reading scores is explained by teaching method? thanks so much
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