Bone mineral densities (mg/cm 2 ) were measured on a sample of n = 9 women (age
ID: 3130742 • Letter: B
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 1125. Let = 0.01
A) The variable (type and level) of interest in this study is:
B) This study can be classified as: Controlled experiment or Observational study
C) The appropriate null/alternative hypothesis pair for this study is:
D) The test statistic for this data set is:
Note: Round your answer to the nearest hundredth.
E) The P-value for this study is:
Note: Round your answer to four places.
Explanation / Answer
a)
It is a quantitative variable at ratio level. [ANSWER]
(It is a ratio level because the lwoest mineral bone density is 0.)
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b)
It is a controlled experiment, as the subjects took the drug conjugated equine estrogen (CEE) for 3 years.
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c)
Formulating the null and alternative hypotheses,
Ho: u <= 1125
Ha: u > 1125 [ANSWER]
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d)
As we can see, this is a right tailed test.
Getting the test statistic, as
X = sample mean = 1134.111111
uo = hypothesized mean = 1125
n = sample size = 9
s = standard deviation = 9.453100608
Thus, t = (X - uo) * sqrt(n) / s = 2.891467516 [ANSWER]
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e)
Thus, getting the critical t,
df = n - 1 = 8
Hence, the p value is
p = 0.010076865 [ANSWER]
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