Homework Answers
Solution:
The 99% confidence interval for population percentage is given as follows:
Where, p̂ is sample percentage, q̂ = 100 - p̂, n is sample size and Z(0.01/2) is critical z-value to construct 99% confidence interval.
Sample percentage of students of PPPP who received more than 80 for the final exam is, p̂ = (12/60)×100 = 20%
q̂ = 100 - 20 = 80% and n = 60
Using Z-table we get, Z(0.01/2) = 2.58
Hence, 99% confidence interval to estimate the percentage of all students of PPPP who received more than 80 for the final exam of the basic statistics course during the last 10 years is,
On rounding to nearest integer we get, confidence interval as
Hence, 99% confidence interval estimate of the percentage of all students of PPPP who received more than 80 for the final exam of the basic statistics course during the last 10 years is, 7% to 33%.
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