Question
In: Statistics and Probability
Suppose a random sample of size 40 was drawn from a normally distributed population, with a...
Suppose a random sample of size 40 was drawn from a normally distributed population, with a known population standard deviation of σ=6.4.
a) What is the margin of error for a 95% confidence level?
Round your response to at least 3 decimal places.
b) What is the margin of error for a 90% confidence level?
Round your response to at least 3 decimal places.
Solutions
Expert Solution
Solution
Given that,
= 6.4
n = 40
a ) At 95% confidence level the z is ,
=
1 - 95% = 1 - 0.95 = 0.05
/ 2 = 0.05 / 2 = 0.025
Z/2
= Z0.025 = 1.960
Margin of error = E = Z/2*
(
= 1.960 * (6.4 /
Margin of error = 1.983
b ) At 90% confidence level the z is ,
= 1 - 90% = 1 - 0.90 = 0.10
/ 2 = 0.10 / 2 = 0.05
Z/2
= Z0.05 = 1.645
Margin of error = E = Z/2*
(
= 1.645* (6.4 /
Margin of error = 1.664
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