"Meeting Mr. Farmer versus Meeting a Farmer: Specific Effects of Aging on Learning Proper Names," published in Psychology and Aging in September 2004, describes an experiment where young and older adults were tested on ability to remember the correct name and occupation to match a set of pictures of faces. The number of passes through the set of sixteen faces needed by the 16 younger adults to retain all the names and occupations had mean 8.38, standard deviation 2.63, and so a 95% confidence interval for population mean is (7.72, 9.04). "Pilot testing indicated that older adults had considerable difficulty learning 16 names and occupations and that they found the experiment distressing. Therefore, each older participant was presented only 12 stimuli."27 The number of passes through a set of twelve faces needed by the 16 older adults to retain them all had mean 10.75, standard deviation 2.72, and so a 95% confidence interval for population mean is (10.07, 11.43).
a. Sketch a line showing possible mean scores (from about 7 to about 12) and use the reported confidence intervals to indicate the range of plausible means for all younger adults and the range of plausible means for all older adults.
b. What is it about the two intervals that suggests it is not plausible for the two population means to be equal?
c. If the sample sizes had been larger, would it be more likely or less likely for the intervals to overlap?
d. If the standard deviations had been larger, would it be more likely or less likely for the intervals to overlap?
e. If the sample means (8.38 and 10.75) had been farther apart, would it be more likely or less likely for the intervals to overlap?