In: Statistics and Probability
n = sample size = 4500
p = proportion of students cheadted at least once = 0.74
x = number of students cheated at least once = n * p = 4500 * 0.74 = 3330
a)
Confidence level = c =0.90
Steps to find 90% confidence interval for the level of cheating among high school students from TI - 84 calculator is
Press STAT>TESTS> Scoll down and select A : 1-PropZInt >
x : 3330
n : 4500
C- level : 0.90
After you have entered all of this information, highlight Calculate. Press Enter.
Output : (0.7292, 0.7508) (Round to 4 decimal)
90% confidence interval for the level of cheating among high school students is (0.7292, 0.7508)
b) Interpretation:
We are 90% confident that true proportion of level of cheating among high school students will lie between (0.7292, 0.7508).
c)
Using all steps as above, just enter C - level = 0.95
Output will be (0.7272, 0.7528)
95% Confidence interval is (0.7272, 0.7528)
Width of 90% Confidence interval = 0.7508 - 0.7292 = 0.0216
Width of 95% Confidence interval = 0.7528 - 0.7272 = 0.0257
Width of 95% Confidence interval is greater than 90% Confidence interval.
95% Confidence interval is more wider than 90% Confidence interval.
95% confidence interval would be wider than 90% Confidence interval.