When σ is unknown and the sample is of size n ≥ 30, there are two methods for computing confidence intervals for μ. Method 1: Use the Student's t distribution with d.f. = n − 1. This is the method...


When σ is unknown and the sample is of size
n
≥ 30, there are two methods for computing confidence intervals for μ.



Method 1: Use the Student's
t
distribution with
d.f.
=
n
− 1.


This is the method used in the text. It is widely employed in statistical studies. Also, most statistical software packages use this method.




Method 2: When
n
≥ 30, use the sample standard deviation
s
as an estimate for σ, and then use the standard normal distribution.


This method is based on the fact that for large samples,
s
is a fairly good approximation for σ. Also, for large
n, the critical values for the Student's
t
distribution approach those of the standard normal distribution.

Consider a random sample of size
n
= 36, with sample mean x = 45.6 and sample standard deviation
s
= 6.5.


(d) Now consider a sample size of 81. Compute 90%, 95%, and 99% confidence intervals for μ using Method 1 with a Student's
t
distribution. Round endpoints to two digits after the decimal.























90%95%99%
lower limit
upper limit



(e) Compute 90%, 95%, and 99% confidence intervals for μ using Method 2 with the standard normal distribution. Use
s
as an estimate for σ. Round endpoints to two digits after the decimal.























90%95%99%
lower limit
upper limit


Jun 01, 2022
SOLUTION.PDF

Get Answer To This Question

Related Questions & Answers

More Questions »

Submit New Assignment

Copy and Paste Your Assignment Here