A random dot stereogram is defined in Wikipedia as a "pair of images of random dots which when viewed with the aid of a stereoscope, or with the eyes focused on a point in front of or behind the images, produces a sensation of depth, with objects appearing to be in front of or behind the display level". An experiment was done to see how different kinds of information about the embedded object would affect the time it takes a viewer to fuse the two images and see the object.
Two groups were tested. Group A was given only a verbal description of the embedded object. Group B was given the same verbal description, but was also shown a drawing of the object. The measured response was the time in seconds it took for each subject to see the object in the stereogram.
Summary statistics for the individual measurements in each group follow.
Group A B
Size Na=43 Nb=35
Mean X'a = 8.56 X'b = 5.55
Standard Deviation Sa = 8.09 Sb=4.8
a. Explain whether or not it seems reasonable to apply the Central Limit Theorem (CLT) to each of the two groups. Discuss the assumptions required to justify using the CLT.
b. Assuming the CLT does apply to both samples, what are the distributions of the means for each group? Show how the standard deviations are calculated.
c. What is the distribution for the difference between the two sample means? Specify the distribution, and give the numerical values of the mean and standard deviation. Justify the distribution chosen. Show the explicit calculation of the standard deviation, and state any assumptions required to justify the calculation.
d. Find the probability that the mean difference (X'a - X'b) is greater than 5 seconds. Explain how you get your answer.