You are going to estimate how long a person holds down a button
on their calculator by randomly selecting people and asking them to
do something on your calculator (which has a special timer to
record how long the enter button is pressed). You practiced on the
people at work and found a standard deviation of about 1.46
seconds. You want to get a 83% confidence interval that is only 0.2
in width. How many people do you need to have in your study?
Remember to always round up on sample size calculations.
Solution :
Given that,
standard deviation = =1.46
Margin of error = E = width / 2 = 0.2/ 2=0.1
At 83% confidence level the z is ,
= 1 - 83% = 1 - 0.83= 0.17
/ 2 = 0.17 / 2 = 0.085
Z/2 = Z0.085 = 1.37
sample size = n = [Z/2* / E] 2
n = ( 1.37*1.46 /0.1 )2
n =400
Sample size = n =400
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