# Sample Size, Margin of Error, Confidence Level

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

Answer: Zc= 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

Answer: sample size = 480

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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