An experimenter is interested in the possible differences betweenmale and female

Question

An experimenter is interested in the possible differences betweenmale and female subjects in their ability to correctly recalldigits that have been read to them (eg, 7, 8, 12, 56, 21, 42, 4,20). To test for gender differences, the experimenter reads outfive different sets of 8 digits to a randomly selected group of 50men and 50 women. After each set is read, the subjects are asked towrite down the digits they can recall. The outcome measure for eachsubject is the total number of correctly recalled digits across thefive sets. For example, a score of 42 (5 sets x 8 digits)represents a perfect score. The mean recall score for the men was33 and for the women was 29.

Using this information, write down the:
a) predictor and dependent variables for this experiment;
b) null and alternative hypotheses for the research;
c) most appropriate statistical test for analysis of thedifferences in recall ability between men and women.
d) conclusion that you would reach regarding the stated hypothesesif the associated significance value of the calculated teststatistic was found to be p= 0.02.
e) Explain what statistical measure you would use to describe themagnitude of any difference that may exist between men and women interms of their ability to correctly recall digits.

Explanation / Answer

The predictor variable is binary. Let a X = 1 denote male, 0denote female. Let Y be the number of digits recalled. Y = + X where is the expected number of digits recalled for femalesand is the expected number of more (less if isnegative) digits that males can recall over females. Null Hypothesis: = 0 (Males and females recall the samenumber of digits) Ha: is not equal to 0 (Males and females recall differentamounts of digits) We can use a t-test here on . p = .02 is very small --> is not equal to 0 --> menand women recall different amounts of digits (we do not know whorecalls more from the p-value alone). We can also use a t-test on the differences of the same means tosee how large this difference in digit recollection likely is.

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