A researcher wants to test the difference of nerve conductivity speed between healthy persons and patients with nerve disorder. Data of nerve conductivity speeds are obtained for each subject. The data x shows the result from 8 healthy subjects, and the data y from 20 disordered subjects.

x = c(40.3,40.0,39.6,40.1,40.7,39.7,40.4,39.8)

y = c(39.4,35.8,37.1,36.8,37.0,37.0,37.1,36.5,37.0,36.2,37.3,35.9,35.7,36.7,35.9,37.7,37.2,38.1,37.0,37.1)

Data set, speed.csv, can be downloaded.

1. Find the standard error of difference estimate if equal variances are

   assumed.

   0.352 0.319 0.234

2. Find the test statistic.

   13.454 8.481 9.89

3. Do you reject the null hypothesis or not? Find the critical value, and complete the hypothesis test with significance level 0.05

   Since the critical value is 2.0555, the null hypothesis can be rejected. Since the critical value is 2.0555, the null hypothesis cannot be rejected. Since the critical value is 2.3646, the null hypothesis cannot be rejected. Since the critical value is 2.3646, the null hypothesis can be rejected.

4. Find an appropriate confidence interval.

   [ 2.495 , 3.805 ] [ 2.265 , 4.035 ] [ 2.607 , 3.693 ]

5. Choose a concluding sentence of the study from the following:

   (i) I can conclude that group of healthy subjects has higher nerve conductivity speeds.
   (ii) I can conclude that group of disordered subjects has higher nerve conductivity speeds.
   (iii) I cannot sufficiently prove that nerve conductivity speeds from two groups are different.

   (iii) (ii) (i)