Question

In: Statistics and Probability

A Rutgers University study found that many high school students cheat on tests. The researchers surveyed...

A Rutgers University study found that many high school students cheat on tests. The researchers surveyed a random sample of 4500 high school students nationwide; 74% of them said they had cheated at least once.
a) Create a 90% confidence interval for the level of cheating among high school students. (Use your calculator to create this interval. Do not do the calculations by hand.)
b) Interpret your interval.
c) Would a 95% confidence interval be wider or narrower? Explain.

Solutions

Expert Solution

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.

orchestra answered 2 years ago
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