Bone mineral densities (mg/cm 2 ) were measured on a sample of n = 9 women (age

Question

Bone mineral densities (mg/cm2) were measured on a sample of n = 9 women (age 45 to 65) with low bone mineral densities (BMD) who had been randomly selected and assigned to a treatment group that took the drug conjugated equine estrogen (CEE) for 3 years. CEE is used as a treatment for low bone density and investigators wanted to examine its effectiveness. The responses, rounded to the nearest integer, are reported in Table 1.

Assuming that this sample is representative of the entire population of women in this age group with low bone density, research clinicians would like to test the hypothesis that, on average, women on CEE therapy will have density levels that are greater than 1320. Let = 0.10

A) The variable (type and level) of interest in this study is:

Quantitative & NominalQuantitative & Ordinal    Quantitative & ContinuousQualitative & DiscreteQualitative & ContinuousQualitative & OrdinalQuantitative & DiscreteQualitative & Nominal

B) This study can be classified as:  ---Select--- Controlled experiment      Observational study

C) The appropriate null/alternative hypothesis pair for this study is:

Ho: = 1320 vs Ha: > 1320Ho: < 1320 vs Ha: 1320    Ho: 1320 vs Ha: > 1320Ho: x 1320 vs Ha: x > 1320Ho: x = 1320 vs x > 1320Ho: 1320 vs Ha: 1320Ho: < 1320 vs Ha: > 1320Ho: = 1320 vs Ha: 1320Ho: 1320 vs Ha: < 1320

Note: you should carry at least 5 decimal precision for any intermediate calculations then round your answer as indicated in the problem

D) The point estimate for the true average BMD for women (age 45 - 65) taking CEE is:

       mg/cm2
     Note: round your answer to the nearest hundredth

E) The point estimate for the true standard deviation for BMD for women (age 45 - 65) taking CEE is:
       mg/cm2
     Note: round your answer to the nearest hundredth

F) The test statistic for this data set is:  
     Note: Round your answer to the nearest hundredth.

G) The P-value for this study is 0.0873. Based on this the statistical decision and English interpretation are:
     Note: You have only 1 submission opportunity for this item

FTR Ha: conclude that CEE therapy increases bone densities in the target population to more than 1320 mg/cm2Reject Ho: conclude that CEE therapy increases bone densities in the target population to more than 1320 mg/cm2     Reject Ha: we cannot conclude that CEE therapy increases bone densities in the target population to more than 1320 mg/cm2FTR Ho we cannot conclude that CEE therapy increases bone densities in the target population to more than 1320 mg/cm2

Table 1: Bone Mineral Densities for women between 45 - 65 years old 1321 1325 1318 1326 1331 1314 1316 1325 1335

Explanation / Answer

Given that,
population mean(u)=1320
sample mean, x =1323.4444
standard deviation, s =6.9121
number (n)=9
null, Ho: =1320
alternate, H1: >1320
level of significance, = 0.1
from standard normal table,right tailed t /2 =1.397
since our test is right-tailed
reject Ho, if to > 1.397
we use test statistic (t) = x-u/(s.d/sqrt(n))
to =1323.4444-1320/(6.9121/sqrt(9))
to =1.495
| to | =1.495
critical value
the value of |t | with n-1 = 8 d.f is 1.397
we got |to| =1.495 & | t | =1.397
make decision
hence value of | to | > | t | and here we reject Ho
p-value :right tail - Ha : ( p > 1.4949 ) = 0.08664
hence value of p0.1 > 0.08664,here we reject Ho
ANSWERS
---------------
null, Ho: =1320
alternate, H1: >1320
test statistic: 1.495
critical value: 1.397
decision: reject Ho
p-value: 0.08664

we have evidence thta women on CEE therapy will have density levels that are greater than 1320

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