Question

The proposed computer mouse designs were compared by recording wrist extension in degrees for 24 people who each used both mouse designs. The erence in wrist extension was calculated by subtracting extension for mouse type 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 14 degrees. Is there convincing evidence that the mean wist extension for mouse type A is greater than for mouse type B Test the relevant hypoteses using a 0.05 significance level (Use .-WAN State the appropriate and alternative hypotheses H -0 MIMO MM-0 M.M. Mo: 0 Mo - 0 CHOMO HAM>0 Find the test statistic and evalue. (Use a table or technology. Round your test s iste toon decimal place and your value to three decimal places.) State the contusion in the problem context We fail to reject M. There is convincing evidence that the mean wrist extension for mouse type A is greater than for mouse type B We reject There is co ng evidence that the man wat extension for mousete A is greater than for more type We fail to reject There is not convincing evidence that the mean wrist extension for mouse type A is greater than for mouse type We reject There is not convincing evidence that the mean wit extension for mouse type A greater than formouse type B (D) Suppose that the standard deviation of the differences was 28 degrees. Is there convincing evidence that the man wrist extension for mouse type A is greater than for mouse type B Test the relevant hypotheses using a 0.05 significance level (se - State the appropriate nuit and alternative hypotheses 0 Wi-

Answer 1

Ans a ) H0:ud=0

And Ha:ud>0

using Minitab >stat>basic stat>paired sample t test

Paired T-Test and CI

N Mean StDev SE Mean
Difference 24 8.82 14.00 2.86

95% lower bound for mean difference: 3.92
T-Test of mean difference = 0 (vs > 0): T-Value = 3.09 P-Value = 0.003

t = 3.09

p-value is 0.003

p value is less than 0.05 so

conclusion: we will reject H0. there is convincing evidence that the mean wrist expansion for mouse A is greater than mouse B

b ) using Minitab

Paired T-Test and CI

N Mean StDev SE Mean
Difference 24 8.82 28.00 5.72

95% lower bound for mean difference: -0.98
T-Test of mean difference = 0 (vs > 0): T-Value = 1.54 P-Value = 0.068

the null and alternative hypothesis is \

H0:ud=0

Ha:ud>0

t = 1.54

p-value = 0.068

the p-value is greater than 0.05

we fail to reject H0. there is convincing evidence that the mean wrist expansion for mouse A is greater than mouse B

c ) option a is true

the larger t-test statistic in part a indicates that it is less likely that, assuming the population mean difference is zero, a difference of 8.82 degrees would be observed when the standard deviation of differences was 14 than when it was 28