The control limits that include 95% of the sample means be,
(19.9671 , 20.0329).
Given, each of 20 people generated a random sample of whole numbers and constructed a 95% confidence interval for the proportion that are odd.
we have to find the confidence interval under confidence of 95%.
Subtract 1 from your sample size. 25 – 1 = 24. This gives you degrees of freedom.
Subtract the confidence level from 1, then divide by two.
(1 – 0.95) / 2 = 0.05
For 24 degrees of freedom (df) and α = 0.05, the result is 1.645.
Divide your sample standard deviation by the square root of your sample size.
0.1 / √(20) = 0.02
Now, 0.02 × 1.645 = 0.0329
The lower end of the range
20 – 0.0329 = 19.9671
The upper end of the range
20 + 0.0329 = 20.0329
Hence, the confidence interval be, (19.9671 , 20.0329)
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