Lerven's test of equality of variances shows:1. The result is significant, so the variances are not different2. The result is significant, so the variances are different3. The result is non-significant, so the variances are not different4. The result is non-significant, so the variances are different From the Levene’s test result, what might you conclude about the use of the t test? 1. The assumption of equal variances is met, so the use of the t test may be appropriate2. The assumption of equal variances is not met, so the use of the t test may be inappropriate3. The assumption of equal variances is not met, so the use of the t test may be appropriate4. The assumption of equal variances is met, so the use of the t test may be inappropriate Group StatisticsStd. ErrorAge in YearsNMeanStd. DeviationMeanMath AchievementLower than 1355650.721612.10574.51340Higher than 1412.51362.5945444350.9457Independent Samples TestLevene's Test for Equality ofVariancest-test for Equality of Means95% Confidence Interval of theDifferenceSignificanceMeanStd. ErrorSig.tdfOne-Sided pTwo-Sided pDifferenceDifferenceLowerUpperMath AchievementEqual variances.671.413-.286997.387.775-.22410.78259-1.759811.31160assumedEqual variances notassumed-.285933.546.388.775-.22410.78553-1.765711.31750Independent Samples Effect Sizes95% Confidence IntervalPointEstimateStandardizerLowerUpperMath AchievementCohen's d12.28823-.018-.143.107Hedges' correction12.29749-.018-.143.107Glass's delta12.51362-.018-143.107a. The denominator used in estimating the effect sizes.Cohen's d uses the pooled standard deviation.Hedges' correction uses the pooled standard deviation, plus a correction factor.Glass's delta uses the sample standard deviation of the control group. How would you report the results?The derived t = 0.41 was significant at p = .05 with df = 997. Therefore, Ho wasrejected, and it was concluded that the mean math achievement score for the olderstudents (12.11) was significantly lower than the mean math achievement score for theyounger students (50.72), t(997) = 0.41, p < .001. In terms of the research question, itappears that younger and older students are different in their level of mathachievement.The derived t = 0.78 was significant at p = .05 with df = 997. Therefore, Ho wasrejected, and it was concluded that the mean math achievement score for the olderstudents (12.51) was significantly lower than the mean math achievement score for theyounger students (50.95), t(997) = 0.78, p < .01. In terms of the research question, itappears that younger students are better at math than older students.The derived t = -0.29 was significant at p = .05 with df = 997. Therefore, Ho wasrejected, and it was concluded that the mean math achievement score for the olderstudents (50.72) was significantly higher than the mean math achievement score for theyounger students (12.11), t(997) = -0.29, p < .000. In terms of the research question, itappears that older students are better at math than younger students.The derived t = 0.67 was not significant at p = .05 with df = 997. Therefore, Ho was notrejected, and it was concluded that the mean math achievement score for the olderstudents (50.72) was not different than the mean math achievement score for theyounger students (50.95), t(997) = 0.67, p > .05. In terms of the research question, itappears that younger and older students are not different in their level of mathachievement.The derived t = -0.29 was not significant at p = .05 with df = 997. Therefore, Ho wasnot rejected, and it was concluded that the mean math achievement score for the olderstudents (50.72) was not different than the mean math achievement score for theyounger students (50.95), t(997) = -0.29, p > .05. In terms of the research question, itappears that younger and older students are not different in their level of mathachievement.

Introduction: Denote σ12, σ22 as the true population variances of the two groups of interest.

Answered: Lerven's test of equality of variances…

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P