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 (0.369, 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 The new confidence interval would be (). (Round to three decimal places as needed.) 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 (). (Round to three decimal places as needed.) c) How would the confidence interval change if the confidence level had been 99% instead of 98%? The new confidence interval would be The new confidence interval would be (Round to three decimal places as needed.)

Explanation / Answer

c) p = 72/160 = 0.45 , n= 160

z value at 99% = 2.576

CI = p + /- z * sqrt ( p * ( 1 -p) / n )

= 0.45 + / - 2.576 * sqrt ( 0.45 * 0.55 / 160)

= (0.348 , 0.551)

The new confidence interval would be wider .The new confidence interval would be(0.348 , 0.551)

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