Frisby and Clatworthy (1975) studied the times that it takes subjects to fuse random-dot stereograms. Random-dot stereograms are pairs of images that appear at first to be random dots. After a subject looks at the pair of images from the proper distance and her eyes cross just the right amount, a recognizable object appears from the fusion of the two images. The experimenters were concerned with the extent to which prior information about the recognizable object affected the time it took to fuse the images. One group of 43 subjects was not shown a picture of the object before being asked to fuse the images. Their average time was 43 = 8.560 and S2X = 2745.7. The second group of 35 subjects was shown a picture of the object, and their sample statistics were 35 = 5.551 and S2Y = 783.9. The null hypothesis is that the mean time of the first group is no larger than the mean time of the second group, while the alternative hypothesis is that the first group takes longer.
a. Test the hypotheses at the level of significance α0 = 0.01, assuming that the variances are equal for the two groups.
b. Test the hypotheses at the level of significance α0 = 0.01, using Welch’s approximate test.