In: Math

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 1.85 mm, and the
sample standard deviation was 0.57; for *n* = 11 CTS
subjects, the sample mean and sample standard deviation were 2.47
and 0.85, 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 *μ*_{1} for normal
subjects and *μ*_{2} for CTS subjects.)

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 | = | |

P-value | = |

Given that,

mean(x)=1.85

standard deviation , s.d1=0.57

number(n1)=7

y(mean)=2.47

standard deviation, s.d2 =0.85

number(n2)=11

null, Ho: u1 = u2

alternate, H1: u1 ≠ u2

level of significance, alpha = 0.01

from standard normal table, two tailed t alpha/2 =3.71

since our test is two-tailed

reject Ho, if to < -3.71 OR if to > 3.71

we use test statistic (t) = (x-y)/sqrt(s.d1^2/n1)+(s.d2^2/n2)

to =1.85-2.47/sqrt((0.3249/7)+(0.7225/11))

to =-1.8518

| to | =1.8518

critical value

the value of |t alpha| with min (n1-1, n2-1) i.e 6 d.f is
3.71

we got |to| = 1.85181 & | t alpha | = 3.71

make decision

hence value of |to | < | t alpha | and here we do not reject
Ho

p-value: two tailed ( double the one tail ) - Ha : ( p ≠ -1.8518 )
= 0.114

hence value of p0.01 < 0.114,here we do not reject Ho

ANSWERS

---------------

null, Ho: u1 = u2

alternate, H1: u1 ≠ u2

test statistic: -1.8518

critical value: -3.71 , 3.71

decision: do not reject Ho

p-value: 0.114

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 = 5 normal subjects was 1.76 mm, and the
sample standard deviation...

1. What is carpal tunnel syndrome?
2. Which are the risk factors of carpal tunnel syndrome?
3. Describe the symptoms of carpal tunnel syndrome
4. What will happen if carpal tunnel syndrome is not
treated?
5 . What is the treatment for Carpal tunnel syndrome?

1. What is carpal tunnel syndrome?
2. Which are the risk factors of carpal tunnel syndrome?
3. Describe the symptoms of carpal tunnel syndrome
4. What will happen if carpal tunnel syndrome is not
treated?
5 . What is the treatment for Carpal tunnel syndrome?

a 45 year old woman recently underwent a carpal tunnel
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Using a significance level of 0.05 to
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When treating carpal tunnel syndrome, should a patient be
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