Bone mineral densities (mg/cm 2 ) were measured on a sample of n = 9 women (age
ID: 3172152 • 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 1305. Let = 0.025
Note: you should carry at least 5 decimal precision for any intermediate calculations then round your answer as indicated in the problem
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.
Explanation / Answer
E) The point estimate for the true standard deviation for BMD for women (age 45 - 65) taking CEE is:
Formula for Standard deviation is given as below:
SD = Sqrt[(X - mean)^2 / (n – 1)]
Calculation table for computation of SD is given as below:
X
(X - mean)^2
1317
18.77774889
1314
1.777768889
1301
136.1111889
1315
5.444428889
1322
87.11104889
1306
44.44448889
1333
413.4443089
1320
53.77772889
1286
711.1112889
Total
11814
1472
Mean
1312.66667
SD
13.56466
(X - mean)^2 = 1472
(X - mean)^2 / (n – 1) = 1472/8 = 184
SD = sqrt(184) = 13.56
F) The test statistic for this data set is:
The formula for test statistic is given as below:
Test statistic = t = (Xbar - µ) / [SD/sqrt(n)]
We are given,
Xbar = 1312.66667
µ = 1305
SD = 13.56465997
Sample size = n = 9
Test statistic = t = (1312.66667 – 1305) / [13.56465997/sqrt(9)]
Test statistic = t = 7.66667/4.521553322
Test statistic = t = 1.695582496
Test statistic = 1.70
X
(X - mean)^2
1317
18.77774889
1314
1.777768889
1301
136.1111889
1315
5.444428889
1322
87.11104889
1306
44.44448889
1333
413.4443089
1320
53.77772889
1286
711.1112889
Total
11814
1472
Mean
1312.66667
SD
13.56466