Quantitative noninvasive techniques are needed for routinely assessing symptoms
ID: 3315421 • Letter: Q
Question
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 1.95 mm, and the sample standard deviation was 0.52; for n = 10 CTS subjects, the sample mean and sample standard deviation were 2.56 and 0.86, respectively. Does this data suggest that the true average gap detection threshold for CTS subjects exceeds that for normal subjects? State and test the relevant hypotheses using a significance level of 0.01. (Use 1 for normal subjects and 2 for CTS subjects.)
H0: 1 2 = 0
Ha: 1 2 > 0H0: 1 2 = 0
Ha: 1 2 < 0 H0: 1 2 = 0
Ha: 1 2 0H0: 1 2 = 0
Ha: 1 2 0
Calculate the test statistic and determine the P-value. (Round your test statistic to two decimal places and your P-value to three decimal places.)
State the conclusion in the problem context.
Fail to reject H0. The data suggests that the true average gap detection threshold for CTS subjects exceeds that for normal subjects.Fail to reject H0. The data suggests that the true average gap detection threshold for CTS subjects is the same as that for normal subjects. Reject H0. The data suggests that the true average gap detection threshold for CTS subjects exceeds that for normal subjects.Reject H0. The data suggests that the true average gap detection threshold for CTS subjects is the same as that for normal subjects.
t = P-value =Explanation / Answer
Result:
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 1.95 mm, and the sample standard deviation was 0.52; for n = 10 CTS subjects, the sample mean and sample standard deviation were 2.56 and 0.86, respectively. Does this data suggest that the true average gap detection threshold for CTS subjects exceeds that for normal subjects? State and test the relevant hypotheses using a significance level of 0.01. (Use 1 for normal subjects and 2 for CTS subjects.)
Ha: 1 2 < 0 H0: 1 2 = 0
Lower tail test used.
Calculate the test statistic and determine the P-value. (Round your test statistic to two decimal places and your P-value to three decimal places.)
t
=
-1.67
P-value
=
0.058
State the conclusion in the problem context.
.
Fail to reject H0. The data suggests that the true average gap detection threshold for CTS subjects is the same as that for normal subjects.
Pooled-Variance t Test for the Difference Between Two Means
(assumes equal population variances)
Data
Hypothesized Difference
0
Level of Significance
0.01
Population 1 Sample
Sample Size
7
Sample Mean
1.95
Sample Standard Deviation
0.52
Population 2 Sample
Sample Size
10
Sample Mean
2.56
Sample Standard Deviation
0.86
Intermediate Calculations
Population 1 Sample Degrees of Freedom
6
Population 2 Sample Degrees of Freedom
9
Total Degrees of Freedom
15
Pooled Variance
0.5519
Standard Error
0.3661
Difference in Sample Means
-0.6100
t Test Statistic
-1.6662
Lower-Tail Test
Lower Critical Value
-2.6025
p-Value
0.0582
Do not reject the null hypothesis
t
=
-1.67
P-value
=
0.058