The mean and standard deviation of a random sample of n measurements are equal t
ID: 3183576 • Letter: T
Question
The mean and standard deviation of a random sample of n measurements are equal to 33.3 and 3.4, respectively.
a. Find a 90% confidence interval for if n = 100. (Round to three decimal places as needed.)
b. Find a 90% confidence interval for if n = 400. (Round to three decimal places as needed.)
c. Find the widths of the confidence intervals found in parts a and b. What is the effect on the width of a confidence interval of quadrupling the sample size while holding the confidence coefficient fixed?
Explanation / Answer
mean = 33.3
std. dev. = 3.4
(A)
For 90% CI, z-value = 1.64
lower limit = 33.3 - 1.64*3.4/sqrt(100) = 32.742
upper limit = 33.3 + 1.64*3.4/sqrt(100) = 33.858
(B)
for n = 400
lower limit = 33.3 - 1.64*3.4/sqrt(400) = 33.021
upper limit = 33.3 + 1.64*3.4/sqrt(400) = 33.579
In (A) CI width = 1.1152
In (B) CI width = 0.5576
As sample size increases CI width decreases
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