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.
![\begin{tabular} {|c|c|c|c|} Drawing (x)&$\bar{x}$&$x-\bar{x}$&$(x-\bar{x})^2\\[1ex] 2,2,2&2&-2.5&6.25\\ 2,2,3&2.3&-2.2&4.84\\ 2,2,5&3&-1.5&2.25\\ 2,2,8&4&-0.5&0.25\\ 2,3,3&2.7&-1.8&3.24\\ 2,3,5&3.3&-1.2&1.44\\ 2,3,8&4.3&-0.2&0.04\\ 2,5,5&4&-0.5&0.25\\ 2,5,8&5&0.5&0.25\\ 2,8,8&6&1.5&2.25\\ 3,3,3&3&-1.5&2.25\\ 3,3,5&3.7&-0.8&0.64\\ 3,3,8&4.7&0.2&0.04\\ 3,5,5&4.3&-0.2&0.04\\ 3,5,8&5.3&0.8&0.64\\ 3,8,8&6.3&1.8&3.24\\ 5,5,5&5&0.5&0.25\\ 5,5,8&6&1.5&2.25\\ 5,8,8&7&2.5&6.25\\ 8,8,8&8&3.5&12.25\\ \end{tabular}](https://tex.z-dn.net/?f=%5Cbegin%7Btabular%7D%0A%7B%7Cc%7Cc%7Cc%7Cc%7C%7D%0ADrawing%20%28x%29%26%24%5Cbar%7Bx%7D%24%26%24x-%5Cbar%7Bx%7D%24%26%24%28x-%5Cbar%7Bx%7D%29%5E2%5C%5C%5B1ex%5D%0A2%2C2%2C2%262%26-2.5%266.25%5C%5C%0A2%2C2%2C3%262.3%26-2.2%264.84%5C%5C%0A2%2C2%2C5%263%26-1.5%262.25%5C%5C%0A2%2C2%2C8%264%26-0.5%260.25%5C%5C%0A2%2C3%2C3%262.7%26-1.8%263.24%5C%5C%0A2%2C3%2C5%263.3%26-1.2%261.44%5C%5C%0A2%2C3%2C8%264.3%26-0.2%260.04%5C%5C%0A2%2C5%2C5%264%26-0.5%260.25%5C%5C%0A2%2C5%2C8%265%260.5%260.25%5C%5C%0A2%2C8%2C8%266%261.5%262.25%5C%5C%0A3%2C3%2C3%263%26-1.5%262.25%5C%5C%0A3%2C3%2C5%263.7%26-0.8%260.64%5C%5C%0A3%2C3%2C8%264.7%260.2%260.04%5C%5C%0A3%2C5%2C5%264.3%26-0.2%260.04%5C%5C%0A3%2C5%2C8%265.3%260.8%260.64%5C%5C%0A3%2C8%2C8%266.3%261.8%263.24%5C%5C%0A5%2C5%2C5%265%260.5%260.25%5C%5C%0A5%2C5%2C8%266%261.5%262.25%5C%5C%0A5%2C8%2C8%267%262.5%266.25%5C%5C%0A8%2C8%2C8%268%263.5%2612.25%5C%5C%0A%5Cend%7Btabular%7D)
