A study was performed to test eyewitness accuracy. Ten pairs of participants entered a room believing they would be participating in a gambling experiment. Each participant was given $10 in coins to play poker with. The participants were randomly seated near the door or away from the door. After 15 minutes, an actor dressed in street clothes burst into the room and stole the money from the participant near the door. The “thief” was later caught, and both participants (the victim and the witness) were asked to identify him in a line-up. Eyewitness accuracies from the participants were then compared. The ten victims reported a mean accuracy of 31.5 (SD = 21). The witnesses had a mean accuracy of 52.2 (SD = 19.5). Was there a difference? What was the effect size of eyewitness accuracy? Show the nul and alternative hypthoesis, aplhpa level 0.05 and test the null hypothtesis and draw the rejctin line, conclusion and effect size

Definition Definition Measure of central tendency that is the average of a given data set. The mean value is evaluated as the quotient of the sum of all observations by the sample size. The mean, in contrast to a median, is affected by extreme values. Very large or very small values can distract the mean from the center of the data. Arithmetic mean: The most common type of mean is the arithmetic mean. It is evaluated using the formula: μ = 1 N ∑ i = 1 N x i Other types of means are the geometric mean, logarithmic mean, and harmonic mean. Geometric mean: The nth root of the product of n observations from a data set is defined as the geometric mean of the set: G = x 1 x 2 ... x n n Logarithmic mean: The difference of the natural logarithms of the two numbers, divided by the difference between the numbers is the logarithmic mean of the two numbers. The logarithmic mean is used particularly in heat transfer and mass transfer. ln x 2 − ln x 1 x 2 − x 1 Harmonic mean: The inverse of the arithmetic mean of the inverses of all the numbers in a data set is the harmonic mean of the data. 1 1 x 1 + 1 x 2 + ...