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# Sample Size, Margin of Error, Confidence Level

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Sample Size, Margin of Error, Confidence Level. See attached file for full problem description.

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1

Confidence level= 98%
or Significance level alpha (a) = 0.02
No of tails= 2
Z value corresponding to 0.02 significance level and 2 tails= 2.3263

2 Margin of error= 3-2.7= 0.3

3 Sample size

Standard deviation =s= 17
confidence interval= 99%
Z corresponding to 99% and two tailed test is 2.5758
We have to ensure that Z* sx < 2
or sx < =2/Z
or sx < 0.776458 =2/2.5758
But
sx=standard error of mean=s/square root of n
s= 17

or n=(s^2)/(sx^2)= 480 =17^2/0.776458^2

4
Standard deviation =s= 3.6
sample size=n= 10
sx=standard error of mean=s/square root of n= 1.1384 = ( 3.6 /square root of 10)
Significance level=alpha (a) = 0.1 =1-0.9
No of tails= 2

Since sample size= 10 < 30
and we are estimating the population standard deviation from sample standard deviation
we will use t distribution
t at the 0.1 level of significance and 9 degrees of freedom (=n-1) and2 tailed test= 1.8331
...

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