Question

In each of the following exercises, complete the ten-step hypothesis testing procedure. State the assumptions that are necessary for your procedure to be valid. For each exercise, as appropriate, explain why you chose a one-sided test or a two-sided test. Discuss how you think researchers or clinicians might use the results of your hypothesis test. What clinical or research decisions or actions do you think would be appropriate in light of the results of your test?

The purpose of a study by Ingle and Eastell (A-10) was to examine the bone mineral density (BMD) and ultrasound properties of women with ankle fractures. The investigators recruited 31
postmenopausal women with ankle fractures and 31 healthy postmenopausal women to serve as controls. One of the baseline measurements was the stiffness index of the lunar Achilles. The mean stiffness index for the ankle fracture group was 76.9 with a standard deviation of 12.6. In the control group, the mean was 90.9 with a standard deviation of 12.5. Do these data provide sufficient evidence to allow you to conclude that, in general, the mean stiffness index is higher in healthy postmenopausal women than in postmenopausal women with ankle fractures? Let alpha =.05

Answer 1

Given that,
mean(x)=90.9
standard deviation , s.d1=12.5
number(n1)=31
y(mean)=76.9
standard deviation, s.d2 =12.6
number(n2)=31
null, Ho: u1 = u2
alternate, H1: u1 > u2
level of significance, α = 0.05
from standard normal table,right tailed t α/2 =1.697
since our test is right-tailed
reject Ho, if to > 1.697
we use test statistic (t) = (x-y)/sqrt(s.d1^2/n1)+(s.d2^2/n2)
to =90.9-76.9/sqrt((156.25/31)+(158.76/31))
to =4.3918
| to | =4.3918
critical value
the value of |t α| with min (n1-1, n2-1) i.e 30 d.f is 1.697
we got |to| = 4.39184 & | t α | = 1.697
make decision
hence value of | to | > | t α| and here we reject Ho
p-value:right tail - Ha : ( p > 4.3918 ) = 0.00006
hence value of p0.05 > 0.00006,here we reject Ho
ANSWERS
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null, Ho: u1 = u2
alternate, H1: u1 > u2
test statistic: 4.3918
critical value: 1.697
decision: reject Ho
p-value: 0.00006
we have enough evidence to support the claim that the mean stiffness index is higher in healthy postmenopausal women than in postmenopausal women with ankle fractures