a) The required Sample Size is 40.
b) the required Sample Size is 62.
Step-by-step explanation:
Given the data in the question;
standard deviation σ = 4 minutes
a)
margin of error E = 75 seconds = ( 75 / 60 )minutes = 1.25 minutes
And 95% confidence.
Now, the Critical Value of z for 0.95 confidence interval;
∝ = 1 - 0.95 = 0.05
= 1.96
so, sample size n will be;
n = [ × σ/E ]²
we substitute;
n = [ 1.96 × (4/1.25) ]²
n = [ 1.96 × 3.2 ]²
n = [ 6.272 ]²
n = 39.338
Since we referring to a number of samples, it approximately becomes 40
Therefore, the required Sample Size is 40
b)
margin of error E = 1 minutes
And 95% confidence.
Now, the Critical Value of z for 0.95 confidence interval;
∝ = 1 - 0.95 = 0.05
= 1.96
so, sample size n will be;
n = [ × σ/E ]²
we substitute;
n = [ 1.96 × (4/1) ]²
n = [ 1.96 × 4 ]²
n = [ 7.84 ]²
n = 61.466
Since we referring to a number of samples, its approximately becomes 62.
Therefore, the required Sample Size is 62.
Sample size determination involves choosing the number of observations or repetitions to include in a statistical sample.
The sample size is an important feature of any experimental study where the goal is to draw conclusions about a population from a sample.
Learn more about Sample Size here: brainly.com/question/17203075
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