Question

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 64 B 59 C 58 D 55 E 72 F 54 G 66 A) Assuming that these participants can be considered to be normally distributed, and that they come from a population with a σ=6.01 years,

calculate a 99% confidence interval for the mean age of the population for which they represent. (Example answer ##.##,##.##)

B) With the same assumptions listed above, calculate a 95% confidence interval for the mean age of the population for which they represent.

(Example answer ##.##,##.##)

C) With the same assumptions listed above, calculate a 90% confidence interval for the mean age of the population for which they represent.

Answer 1

Solution: Given that 64,59,58,55,72,54,66

X = 61.14, σ = 6.01, n = 7

A) 99% Confidence interval for Z = 2.576

99% Confidence interval for the mean = X +/- Z*σ/sqrt(n)
= 61.14 +/- 2.576*6.01/sqrt(7)
= (55.29, 66.99)

B) 95% Confidence interval for Z = 1.96

99% Confidence interval for the mean = X +/- Z*σ/sqrt(n)
= 61.14 +/- 1.96*6.01/sqrt(7)
= (56.69 , 65.59)

C) 90% Confidence interval for Z = 1.645

90% Confidence interval for the mean = 61.14 +/- 1.645*6.01/sqrt(7)
= (57.40 , 64.88)