e t Lest for Iwo Kelated Samples Due Today at 1 1:59 PM MST Assume that the data
ID: 3356091 • Letter: E
Question
e t Lest for Iwo Kelated Samples Due Today at 1 1:59 PM MST Assume that the data satisfy all of the required assumptions for a repeated-measures t test. The graduate studert calculates the following statistics for her hypothesis test: Mean difference (Mo) 0.04 Estimated population standard deviation of the differences (s) 0.08 Estimated standard error of the mean differences (SwD) Degrees of freedom (df) The t statistic The critical values of t when = 05 0.0089 80 4.49 +1.990 Natice that significant when t since the t statistic (4.49) is in the crtical region (t 1.990), the hypothesis test is 05. A 95% confidence interval for the mean difference is Use Cohen's d to calculate the effect size. The absolute value of the estimated d is criteria, this is a Using Cohen's effect size. Use r? to calculate the effect size. The r2 is variability in the peripheral visual perception is explained by whether it was measured before or after playing the action video game. (Round to the nearest percent.) This value of r2 means that, on average, Y% of the 0 Type here to searchExplanation / Answer
Calculation
M = 0.04
t = 1.99
sM = (0.082/82) = 0.01
= M ± t(sM)
= 0.04 ± 1.99*0.01
= 0.04 ± 0.0176
Result
M = 0.04, 95% CI [0.0224, 0.0576].
You can be 95% confident that the population mean () falls between 0.0224 and 0.0576.
cohen's dtest = Mean difference/pooled variance
=> pooled variance= (SDpooled = ((SD12 + SD22) 2)= sqrt(0.08/2)= 0.2
cohen's d =0.04/0.2= 0.2
Cohen suggested that d=0.2 be considered a 'small' effect size, 0.5 represents a 'medium' effect size and 0.8 a 'large' effect size.
t= r*sqrt(n-2)/sqrt(1-r^2)
4.49= r*sqrt(80)/sqrt(1-r^2)
4.49= r*8.944/sqrt(1-r^2)
4.49/8.94= r/sqrt(1-r^2)
0.5022= r/sqrt(1-r^2)
Squarring both sides, we get
0.2522= r^2/1-r^2
0.2522(1-r^2)=r^2
0.2522-0.2522*r^2= r^2
0.2522= 1.2522r^2
r^2= 0.2522/1.2522
r^2= 0.2014
20.14% indicates that the model explains only 20.14% of the variability of the response data around its mean.
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