Answer:
For 90% CI = (0.428, 0.572)
For 98% CI = (0.399, 0.601)
The confidence interval (and Margin of error) reduces when 90% confidence level is used compared to when 98% confidence level is used.
Step-by-step explanation:
Confidence interval can be defined as a range of values so defined that there is a specified probability that the value of a parameter lies within it.
The confidence interval of a statistical data can be written as.
p+/-z√(p(1-p)/n)
Given that;
Proportion p = 66/132 = 0.50
Number of samples n = 132
Confidence level = 90%
z(at 90% confidence) = 1.645
Substituting the values we have;
0.50 +/- 1.645√(0.50(1-0.50)/132)
0.50 +/- 1.645√(0.001893939393)
0.50 +/- 0.071589436011
0.50 +/- 0.072
(0.428, 0.572)
The 90% confidence level estimate of the true population proportion of students who responded "yes" is (0.428, 0.572)
For 90% CI = (0.428, 0.572)
For 98% CI = (0.399, 0.601)
The confidence interval (and Margin of error) reduces when 90% confidence level is used compared to when 98% confidence level is used.
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