Question

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 11 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. H0: μd < 0 Ha: μd > 0 H0: μd = 0 Ha: μd < 0 H0: μd > 0 Ha: μd < 0 H0: μd = 0 Ha: μd ≠ 0 H0: μd = 0 Ha: μd > 0 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.) t = P-value = State the conclusion in the problem context. We reject H0. There is not convincing evidence that the mean wrist extension for mouse type A is greater than for mouse type B. We reject H0. There is convincing evidence that the mean wrist extension for mouse type A is greater than for mouse type B. We fail to reject H0. There is not convincing evidence that the mean wrist extension for mouse type A is greater than for mouse type B. We fail to reject H0. There is convincing evidence that the mean wrist extension for mouse type A is greater than for mouse type B.

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 11 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 u = 4.-H.) State the appropriate null and alternative hypotheses. O Hold< 0 H4>0 O H:40 = 0 н: на < 0 Houd > 0 на: како Houd = 0 4: 40 . Houd = 0 H:H > 0 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.) t = P-value = State the conclusion in the problem context. We reject H. There is not convincing evidence that the mean wrist extension for mouse type A is greater than for mouse type B. We reject H. There is convincing evidence that the mean wrist extension for mouse type A is greater than for mouse type B. We fail to reject H. There is not convincing evidence that the mean wrist extension for mouse type A is greater than for mouse type B. We fail to reject H . There is convincing evidence that the mean wrist extension for mouse type A is greater than for mouse type B.

Answer 1

The statistical software output for this problem is:

One sample T summary hypothesis test: u: Mean of population Ho u0 HA u 0 Hypothesis test results: Sample Mean Std. Err. DF P-value Mean T-Stat 8.82 2.2453656 23 3.9280908 0.0003

Hence,

Hypotheses: Option D is correct.

t = 3.9

P-value = 0.000

Conclusion: Option B is correct.