Please show all work The table below shows the number of hours per day 11 patien

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Please show all work

The table below shows the number of hours per day 11 patients suffered from headaches before and after 7 weeks of soft tissue therapy. At a 0.01, is there enough evidence to conclude that soft tissue therapy helps to reduce the length of time patients suffer from headaches? Assume the samples are random and dependent, and the population is normally distributed. Complete parts (a) through (f) Patient 1 2 3 4 5 6 7 8 9 10 11 Daily headache hours (before) 2.3 4.2 2.3 2.2 2.4 2.7 2.8 3.2 3.7 1.9 25 Daily headache hours (after) 1.8 4.6 1.8 1.6 1.5 1.2 2.7 3.1 1.8 1.2 3.2 a) Identify the claim and state H and H The claim is "The therapy helps to reduce the length of time patients suffer from headaches Let ud be the hypothesized mean of the patients' daily headache hours before therapy minus their daily headache hours after it. State Ho and Ha. Choose the correct answer below. B. Ho: so A. H Ho: ud sd a: d >0 Ha: d d o D. Ho: Hd 20 O E. a: d zd Ho: Hd d Ha: Hd

Explanation / Answer

Solution:

a) the claim is "the therapy helps to reduce the length of time patients suffer from headaches.

according to the claim we must have d > 0

hence the correct hypothesis is
B) H0: d 0
Ha: d > 0

b) Here n=11 observations.
and alpha = 0.01

and the test is right tailed
hence the critical value is t0.01,11-1 which is the upper 0.01 point of a t distribution with df 10

t0.01,10 = 2.764
and since the test is right tailed hence the critical region is t >2.764
d. t >2.764

c) Let X denotes the daily headache hours before therapy Y denotes the same after therapy
let d = X-Y

so dbar = Xbar-Ybar = mean of X-mean of Y= 0.5182

so sd^2 = variance of d = 1/(n-1) (di-dbar)^2

hence sd = sqrt(sd^2) = 1.11

d) hence the test statistic is given by T = (dbar-0)*sqrt(n)/sd which under H0 follows t10

now the value of the test statistic is t=(0.5182-0)*sqrt(11)/1.11 = 1.5484

e) the rejection region is t >2.764

but here t = 1.5484

hence fail to reject the null hypothesis.

f) hence the conclusion is

B. at 1% level of significancw, there is not enough evidence that soft tissue therapy helps toreduce the length of time patients suffer from headaches.

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