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. USE SALT (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 MMA - Mg.) State the appropriate null and alternative hypotheses. O Ho: My > 0 Hai Hoo Ho: Moco Hai Ha > 0 O Ho: H = 0 H:Hd > 0 Hoi Hoo Ho: Md* 0 Оно: на = 0 Hai Mo<0 Find the test statistic and P-value. (Use a table or SALT. Round your test statistic to one decimal place and your P-value to three decimal places.) t = 3.3 P-value - 0.001 State the conclusion in the problem context. We fail to reject Ho. There is convincing evidence that the mean wrist extension for mouse type A is greater than for mouse type B. We fail to reject Ho. There is not convincing evidence that the mean wrist extension for mouse type A is greater than for mouse type B. We reject Ho. There is not convincing evidence that the mean wrist extension for mouse type A is greater than for mouse type B o We reject Ho. There is convincing evidence that the mean wrist extension for mouse type A is greater than for mouse type B (b) Suppose that the standard deviation of the differences was 35 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 o MA - Mg.)

Answer 1

a) We are testing,

H0: ud=0

vs H1: ud>0

Test statistic: (8.82)/(13/√24) = 3.3

P-value of this one sided t n-1 ie t23 test is:

P(t23>3.3) = 0.001 (from t tables)

Since p-value < significance level of 0.05, we have sufficient evidence to Reject H0. So here option d is correct.

b) We are testing,

H0: ud=0

vs H1: ud>0

Test statistic: (8.82)/(35/√24) = 1.2

p-value; P(t23>1.2) = 0.121

Since the p-value here > significance level of 0.05, we fail to reject H0. So option b is correct here.

c) We accept the claim in part a and reject it in part b..so larger test statistic helps us to accept the claim..so option b is correct here.