Question

What would be the right steps for this equation? I’m in elementary statistics so that might help with what equations/set up to help me with.

. Randomly selected students were placed into different testing environments, wa an d the same test s administered to all the students. (This is a standardized test and thus we know the variance should remain constant and th e scores should be distributed normally.) Is there evidence to scores? (12) conclude that the different testing environments resulted in different mean Silent & still Silent with moving people Noisy talking Quiet Instrumental music 78 91 80 89 90 75 82 80 45 59 70 90 72 91 72 56 65 23 80

Answer 1

Но Ha : Atleast two μ differ T1 78 91 T 2 T3 T4 6084 8281 6400 7744 5184 3136 8100 2025 3481 89 7921 7744 5184 8281 75 6724 6400 70 90 72 91 72 65 6400 T2 36 829458 35 430 342 486 39 886 k4 (Number of groups or treatment Conditions) n 24 (Number of data points.) (465 +458342 486)2 24 -(36829354302206039886) 134205 127750.041667 6454.958333 S STotal 6454.9583 4 465 465 465 465 +127750.041667 129858.166667 127750.041667 2108.125 SS Among 2108.125 SSWithin SSTotal SSAmong 6454.958333-2108.1254346.833333 Within4346.8333 Significance level - 0.05 Test statistic, FMSAmoSSAmon/k1 MSWithin 2108.125/3 SSWithin/n-4 4346.833333/20 702.708333 217 341 667 3.233

Test statistic, F-3.233 formulas used in ANOVA table (for demonstration) Source df sS MS MSAmong MSwithin Among k-1 SSAmong MSAmong SSWithisn =-n-r Within n-kSSWithinMSWithin - Total -SS Total ANOVA MS Source df Among Within 204346.833333 217.341667 32108.125 702.7083333.233 Total 236454.958333 Degrees of freedom for Numerator, dfN k-13 Degrees of freedom for Denominator, dfD-n -k 20 To get F-critical-value, we can use excel fucntion F. INV. RT (0.05,3,20) 3.098 Rejection region is to the right of critical value, .e., we reject nl hypothesis if test statistic is greater than 3.098 To get p-value, we can use excel fucntion F,DIST . RT (3.233 197 , 3,20) 0.044 084 416~0.0441 Since test statistic is greater than critical value , we (reject ) null hypothesis At 5% level, there is (sufficient) evidence that atleast one of the means differs from the rest