Quantitative noninvasive techniques are needed for routinely assessing symptoms of peripheral neuropathies, such as carpal tunnel syndrome (CTS). An article reported on a test that involved sensing a tiny gap in an otherwise smooth surface by probing with a finger; this functionally resembles many work-related tactile activities, such as detecting scratches or surface defects. When finger probing was not allowed, the sample average gap detection threshold for m = 7 normal subjects was 1.71 mm, and the sample standard deviation was 0.59; for n = 11 CTS subjects, the sample mean and sample standard deviation were 2.34 and 0.89, respectively. Required:
a. Does this data suggest that the true average gap detection threshold for CTS subjects exceeds that for normal subjects?
b. State and test the relevant hypotheses using a significance level of 0.01. (Use μ1 for normal subjects and μ2 for CTS subjects.) Calculate the test statistic and determine the P-value.