Hello, can you help me with this question about t-test statistic? Thank you.

Your trial-bytrial data On each trial, you indicated the likeability of a face. Different faces were young or old men or women. The nal column gives the likeability rating. Trial Age of face Sex of face Likeability rating 1 Old Male 37.0 2 Old Male 32.0 3 Old Male 23.0 4 Old Male 35.0 5 Young Male 34.0 6 Young Male 33.0 7 Old Female 29.0 8 Young Female 30.0 9 Young Male 31 .0 10 Old Female 32.0 1 1 Old Female 6.0 12 Young Female 32.0 13 Young Female 42.0 14 Old Male 1 9.0 1 5 Young Male 2.0 1 6 Young Male 0.0 1 7 Old Male 1 8 .0 18 Young Male 25.0 1 9 Old Male 32.0 20 Old Female 23.0 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 3? 38 39 40 Young Old Yo u ng Old Young Yo u ng Young Young Old Old Old Yo u ng Old Old Young Young Old Young Old Old Male Female Male Male Female Male Male Female Male Female Female Female Female Female Female Female Female Female Male Female 3?.0 26.0 23.0 2?.0 41.0 34.0 15.0 30.0 26.0 31.0 29.0 27.0 28.0 21.0 25.0 42.0 26.0 33.0 40.0 8.0 41 42 43 44 45 46 47 48 49 50 51 52 53 55 56 57 58 59 60 61 62 63 64 Young Young Young Old Old Old Old You ng Old Young Young Young Young Old Young You ng Old Old Young Old Young Old Old You ng Female Male Female Male Female Female Female Male Male Female Male Female Male Female Female Female Male Female Female Male Male Male Male Male 31.0 12.0 22.0 24.0 24.0 4.0 38.0 23.0 15.0 26.0 0.0 25.0 13.0 3.0 56.0 55.0 55.0 2.0 57.0 7.0 14.0 3.0 16.0 34.0 Most college students are in the young age group, so we expect that they will give higher likeability ratings for the young faces than for the old faces. If you happen to be an older student, you might also show a bias toward higher likeability ratings for young faces, but it will not be as strong as for younger students. The statistical analysis below guides you through a two-sample Heat. The null hypothesis is that the mean likeability rating is the same for young and old faces H03 \"young 'l-lold = O, and the altemative hypothesis is that the mean likeability rating is different for young faces and old faces Ha: \"young 'Uold i 0- We will use a = 0.05. Formulas To calculate the ftest statistic, you need to rst calculate the mean and variance of scores for each condition. This is done in the rst four questions. Next, you need to pool the variances using the following formula 2 _ (n1 Us? + (m Deg n1+n22 '9 a where n, and n2 are the sample sizes (number of trials) for the young and old face conditions. 521 and 522 are the variances for the young and old face conditions. The pooled variance is used to calculate the standard error of the difference of means Now compute the ttest statistic which has degrees of freedom df=n1 + n2 -2. Finally, you can calculate the pvalue for the test statistic. This is most easily done with an online calculator. Be sure to use a two-tailed test. Use the trial-bytrial data to answer these questions. Question Answer Variance of the likeability' for the young faces: (The difference between your answer and the correct value must be less than 0.01.) :[ :l Variance of the likeability for the old faces: :[ (The difference between your answer and the correct value must be less than 0.01.) Standard error of'the difference of means: (The difference between your answer and the correct value must be less than 0.01.) :[ :l degrees of freedom: :[ (Your answer must exactly equal the correct value.) Do you reject the null hypothesis?': I - I [

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