A survey of 160 students is selected randomly on a large university campus. They

Question

A survey of 160 students is selected randomly on a large university campus. They are asked if they use a laptop in class to take notes. The result of the survey is that 72 of the 160 students responded "yes." An approximate 98% confidence interval is (0.359, 0.541). Complete parts a through d below. a) How would the confidence interval change if the confidence level had been 95% instead of 98%? The new confidence interval would be narrower. The new confidence interval would be (.373, .527). b) How would the confidence interval change if the sample size had been 400 instead of 160? (Assume the same sample proportion.) The new confidence interval would be The new confidence interval would be (, ).

Explanation / Answer

The statistical software output for confidence interval is:

One sample proportion confidence interval:
p : Proportion of successes
Method: Standard-Wald

98% confidence interval results:

Hence,

The new confidence interval would be narrower. The new confidence interval would be (0.392, 0.508).

Proportion Count Total Sample Prop. Std. Err. L. Limit U. Limit p 180 400 0.45 0.024874686 0.39213283 0.50786717

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