MeanEPS 625 – INTERMEDIATE STATISTICSPRACTICE t TEST – NO. 2Dr. Kureous, a teacher at George Junior High, now wants to determine if there is asignificant difference between the 6th grade boys and girls in his class on theirmathematics exam. He does not have a prediction as to whether the boys or the girlswill be better – he simply wants to see if they differ significantly on the math exam.1. State (using symbols or words) the null hypothesis and the alternative hypothesis for his mathematics Independent-Samples t Test.H0:Ha:2. Using an a priori alpha () level of .05.2.a. Has Dr. Kureous met the assumption of homogeneity of variance for the Math Exam ttest?YES or NO (circle your answer selection)2.b. Justify/explain your answer – that is, how did you come to your conclusion? (Hint: look at the SPSS printout).3. After computing the test statistic (t-test) – complete the following tables for the Math Exam Independent-Samples t-Test (Do not round – use the values from SPSS):Gender N MeanStandardDeviationStandard Errorof the MeanBoysGirlst dfSig.(2-tailed)MeanDifference95% CI of theDifferenceLower Upper4. Using an alpha () level of .05, interpret the results from the Math Exam t test:4.a. Did you reject the null hypothesis in favor of the alternative hypothesis (indicated in question 1)?YES or NO (circle your answer selection)4.b. Justify your answer, that is, how did you come to your conclusion?DO NOT make reference to the t critical value or the confidence intervals.If applicable (or indicate otherwise and why), calculate the Effect Size – be sure to show your work.2121NNNNtd4.c. Briefly discuss your findings (i.e., what do the results indicate or mean). Be sure to make reference to the group means and include all applicable values. Also include thestatistical string (values and symbols).PRACTICE t TEST – NO. 2PAGE – 2EPS 625 – INTERMEDIATE STATISTICSPRACTICE t TEST – NO. 2Independent-Samples T-TestGroup Statistics15 88.67 6.532 1.68715 80.40 12.642 3.264gender1 Boys2 GirlsmathN Mean Std. DeviationStd. ErrorMeanIndependent Samples Test8.033 .008 2.250 28 .032 8.267 3.674 .740 15.7932.250 20.977 .035 8.267 3.674 .625 15.908Equal variancesassumedEqual variancesnot assumedmathF Sig.Levene's Test forEquality of Variancest df Sig. (2-tailed)MeanDifferenceStd. ErrorDifference Lower Upper95% ConfidenceInterval of theDifferencet-test for Equality of MeansEPS 625 – INTERMEDIATE STATISTICSPRACTICE t TEST – NO. 2Dr. Stats would now like to see if there is a difference between Exam_2 and the Finalfor her entire class. She does not have a prediction as to whether the performance willbe higher or lower for the two exam comparison – she simply wants to determine if theclass performed significantly different on the two test occasions.5. Using an alpha () level of .05, interpret the results from the Exam_2 / Final t test:5.a. Using the Table of Critical Values of Student’s t Distribution – what would the t critical value (tcrit) be for the Exam_2 / Final Dependent-Samples t-Test:5.b. Did you reject the null hypothesis in favor of the alternative hypothesis?YES or NO (circle your answer selection)5.c. Justify your answer, that is, how did you come to your conclusion? You may make reference to any of the three methods of determination. Be sure to include all applicable values for the method that you choose. If applicable (or indicate otherwise and why), calculate the Effect Size – be sure to show your work.SDMeand orNtd 5.d. Briefly discuss your findings (i.e., what do the results indicate or mean). Be sure to make reference to the group means and include all applicable values. Also include thestatistical string (values and symbols).EPS 625 – INTERMEDIATE STATISTICSPRACTICE t TEST – NO. 2Dependent-Samples T-TestPaired Samples Statistics81.33 45 13.915 2.07480.89 45 13.284 1.980Exam_2FinalPair1Mean N Std. DeviationStd. ErrorMeanPaired Samples Correlations45 .227 .134Exam_2 & FinalPair 1N Correlation Sig.Paired Samples Test.444 16.916 2.522 -4.638 5.527 .176 44 .861Exam_2 - FinalPair 1Mean Std. DeviationStd. ErrorMean Lower Upper95% ConfidenceInterval of theDifferencePaired Differencest df Sig.