# confidence intervals

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• Aug 10th 2010, 02:00 PM
sj247
confidence intervals
A random sample of size
n = 21 is taken from a Normal distribution with unknown mean μ

and known variance
= 23.6. The sample mean is 1.3.

(a) Write down the 100(1
− a)% two–sided confidence interval for μ when a= 0.05.

(b) If the length of the confidence interval is not exceed the value 2, what is the sample size that should be taken to ensure this?

(c) Describe the changes to the confidence interval if variance
is unknown and replaced by the

sample variance.

I struggle with part b), and part c)

Any help would be great, thanks
• Aug 10th 2010, 02:18 PM
pickslides
For part b) read this article. PEOD6/PD006: Determining Sample Size

Quote:

Originally Posted by sj247
(c) Describe the changes to the confidence interval if variance[/SIZE][/FONT][/SIZE][/FONT][FONT=CMR10][SIZE=3][FONT=CMR10][SIZE=3]is unknown and replaced by the[/LEFT]
sample variance.

Becomes $\bar{x}\pm t_{df,\alpha}\times \frac{s}{\sqrt{n}}$
• Aug 10th 2010, 03:36 PM
sj247
could you go through part b) in stages please. I've read the material but it hasnt helped.

Thanks