In: Statistics and Probability
Two proposed computer mouse designs were compared by recording wrist extension in degrees for 24 people who each used both mouse designs.† The difference in wrist extension was calculated by subtracting extension for mouse type B from the wrist extension for mouse type A for each person. The mean difference was reported to be 8.82 degrees. Assume that this sample of 24 people is representative of the population of computer users.
(a)
Suppose that the standard deviation of the differences was 13 degrees. Is there convincing evidence that the mean wrist extension for mouse type A is greater than for mouse type B? Test the relevant hypotheses using a 0.05 significance level. (Use
μd = μA − μB.)
State the appropriate null and alternative hypotheses.
Find the test statistic and P-value. (Use a table or technology. Round your test statistic to one decimal place and your P-value to three decimal places.)
State the conclusion in the problem context.
b.
Suppose that the standard deviation of the differences was 33 degrees. Is there convincing evidence that the mean wrist extension for mouse type A is greater than for mouse type B? Test the relevant hypotheses using a 0.05 significance level. (Use
μd = μA − μB.)
State the appropriate null and alternative hypotheses.
Find the test statistic and P-value. (Use a table or technology. Round your test statistic to one decimal place and your P-value to three decimal places.)
State the conclusion in the problem context.