To test if shift work leads to increase in caloric intake, a dietician had 20 of her clients record the amount of calories they consumed during the day. She believed those who work at night consumed more calories. The data below are in hundreds of calories. Is there a significant difference among the caloric inputs? DAY NIGHTBOYS: 44 42 45 41 41 41 39 36 40 36 GIRLS: 48 60 49 52 47 52 53 42 52 60More info:-critical value of F : 4.493998-obtained value of the interaction F= 12.033 What is the significance level of the homogeneity of variances test?Is the assumption violated? GenderDescriptive StatisticDependent Variable: caloriesGender day_night| Mean Std. Deviation N1.001.002.0053.20007.429670539.20002.9495805Total46.20009.101890 102.5884401.002.002.0049.8000553.20007.4296705Total51.50005.542760 10Total1.002.0051.500046.20005.542760 109.101890 10Total48.85007.82220 20Levene's Test of Equality of Error Variances"LeveneStatisticdf1df2Sigcalories Based on Mean1.688316 210Based on Median1.155316 .358Based on Median and1.155 310.966 |.371with adjusted dfBased on trimmed mean1.80316.188Tests the null hypothesis that the error variance of the dependent variable is equal acrossgroups,a. Dependent variable: caloriesb. Design: Intercept + Gender + day_night + Gender * day_nightTests of Between-Subjects EffectsDependent Variable: caloriesТуре III Sumof Squares659.350*Partial EtaSourcedf Mean SquareSig.6.988 .003FSquaredCorrected Model219.78356747726.45047726.450 1517.534 .000InterceptGenderday nightGender * day_night.990140.450140.4504.466.051.218140.450140.4504.466 .051218378.450378.45012.033 .003.429Error503.200 1631.450Total48889.000 20Corrected Total1162.550 19Tests of Between-Subjects EffectsDependent Variable: caloriesSourceNoncent. Parameter Observed PowerCorrected Model20.965.9391.000510Intercept1517.534Gender4.466Day nightGender day night4.46651012.033902ErrorTotalCorrected Totala. R Squared = .567 (Adjusted R Squared = 486)b. Computed using alpha = .05

Comment on the results of homogeneity of variances test: The response variable is amount of calories consumed. The predictor variables are gender, day_night and gender*day_night. One of the most important assumptions of multiple linear regression is Homogeneity of variances.Explanation: Since, the level is significance is not specified, the prior level of significance α = 0.05 can be used. Thus, the significance level is 0.05. Levene’s test is used to test the homogeneity of error variance. Here, the P-values based on mean, median, median with adjusted df and trimmed mean are 0.210, 0.358, 0.371 and 0.188. Here, all the P-values are greater than the level of significance 0.05. Therefore, there will not be enough evidence to reject the null hypothesis “Error variance of the dependent variable is equal across groups”. Thus, the assumption of equality of variances is not violated.