Answer
(A) Using TI-84, press STAT, then TESTS, then 1-PropZTest
enter the data
x: 75
n: 300
c = 0.99
Click on CALCULATE
we get
(0.1856, 0.3144)
We are 99% confident that the true proportion of erros made by beginning programming students that are punctuation erros is between 0.1856 and 0.3144
(B) Using TI-84, press STAT, then TESTS, then 1-PropZTest
enter the data
x: 75
n: 300
c = 0.95
Click on CALCULATE
we get
(0.201,0.299)
this interval is shorted as compared to the 99% confidence interval
(C) z score for 99% confidence interval is 2.58, sample size is n = 300 and p = 75/300 = 0.25
Margin of error for 99% =
z score for 95% confidence interval is 1.96, sample size is n = 300 and p = 75/300 = 0.25
Margin of error for 99% =
(D) Margin of error from part (B) = (Upper limit- lower limit)/2 = (0.299-0.201)/2 = 0.049
Yes, both the margin of errors are same. This is because both the methods providing us exactly same value using same input data
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