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 tinygap 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 notallowed, the sample average gap detection threshold for m = 5 normal subjects was 1.62 mm, and the sample standard deviation was 0.53; for n = 10 CTS subjects, the sample mean and sample standarddeviation were 2.36 and 0.85, respectively. Does this data suggest that the true average gap detection threshold for CTS subjects exceeds that for normal subjects?USE SALTState and test the relevant hypotheses using a significance level of 0.01. (Use μ₁ for normal subjects and 2 for CTS subjects.)0 Но М1-М2=0Hải My My 20| Ho: M₁ M₂ = 0на: H1 - H2#0о но: 41-H2=0Hải My M2 > 0ⒸH₁ H₁ H₂ = 0H₂: M₁ - H₂ <0Calculate the test statistic and determine the P-value. (Round your test statistic to one decimal place and your P-value to three decimal places.)t =P-value=

The random sample of normal subjects, The sample mean, The sample standard deviation, The random sample of CTS subjects, The sample mean, The sample standard deviation, The level of significance, The pooled variance is computed as follows:The degrees of freedom is computed as follows:The null and alternative hypotheses are:The test statistic is computed as follows:Thus, the test statistic is, P-value:- The p-value is computed using the R software. The R code and the results are given below:1> pt(q=-1.764006,df=13,lower.tail=TRUE) 2[1] 0.0506004Thus, the p-value is .Conclusion:-Here the . So, we fail to reject the null hypothesis. Therefore, there is insufficient evidence to conclude that the true average gap detection threshold for CTS subjects exceeds that for normal subjects.Note:- Assuming the population variances are equal. So, we used the above test statistic here.The null and alternative hypotheses are:The test statistic is, The p-value is Conclusion:-Fail to reject the null hypothesis. Therefore, there is insufficient evidence to conclude that the true average gap detection threshold for CTS subjects exceeds that for normal subjects.