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Statistics and Analytics eleven Questions(solved)
1. The following table illustrates the BMI for a number of patients recently enrolled in a
study investigating the relationship between BMI and type 2 diabetes.
Participant BMI (kg/m2) A
A) Assuming the participants can be considered to be normally distributed, and that they come from a population with a σ=2.4 kg/m2, calculate a 95% confidence interval for the mean BMI of the population for which they represent.
26.5 + 19.2 + 29.7 + 27.4 + 30.2 + 28.9
P [𝑋̅ −
< 𝜇 < 𝑋̅ + 𝑍
] = 0.95
𝑋̅ − 1.96 𝑥
26.983 − 1.96 𝑥
B) Correctly interpret the confidence interval you found above.
The interval found above shows that the likelihood of having the mean in
this interval is 0.95 implies with 95 percent certainty that the mean BMT would reside in this interval.
2. Suppose the following table illustrates the ages for a number of participants projected to enroll into a clinical trial looking at early onset of dementia.
Patient Age A
A) Assuming that these participants can be considered to be normally distributed, and that they come from a population with a σ=4.3 years, calculate a 99% confidence interval for the mean age of the population for which they represent.
n = 7 99% Confidence interval
64 + 57 + 58 + 53 + 71 + 54 + 63(420)
𝑍𝛼12 = 2.58 4.3
= 60 ± (2.575 ∗
B) With the same assumptions listed above, calculate a 90% confidence interval for the mean age of the population for which they represent.
= 60 ± (1.645 ∗
C) Compare the precision of the two confidence intervals.
The confidence interval for 90% is more precise because the interval is relatively narrow (5.347) and the confidence interval of 99% (8.37) has greater uncertainty because the interval was wider.
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