In three algebra classes, 51 out of 87 students reported their enrollment status

Question

In three algebra classes, 51 out of 87 students reported their enrollment status as full-time. The instructor, Jeff Lacks, would like to estimate the proportion of algebra students who are enrolled full-time with 90% confidence. (a) Use Jeff's data to construct a 90% confidence interval for the proportion of algebra students who are enrolled full-time. (b) Jeff's colleagues are interested in these data, but they'd like a more accurate estimate. For more accuracy, how should Jeff adjust i. the sample size? ii. the confidence level?

Explanation / Answer

a) X = 51 , n = 87

p^ = X /n = 51 /87 = 0.5862

Confidence Interval = p ± Z/2 × [(p×q)/n] ,

z = 1.645

(0.499 , 0.673 )

b) for more accuracy

we need to decrease margin of error

margin of error = Z/2 × [(p×q)/n] ,

hence we have to 1) increase sample size {n is in denominator }

2) decrease confidence level . { z is directly proportional to confidence level}

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