A university dean is interested in determining the...

A university dean is interested in determining the proportion of students who receive some sort of financial aid. Rather than examine the records for all students, the dean randomly selects 200 students and finds that 118 of them are receiving financial aid. If the dean wanted to estimate the proportion of all students receiving financial aid to within ± 0.04 with 99.51% reliability, how many students would need to be sampled? A. n = 41 B. n = 1,007 C. n = 1,844 D. n = 1,006

Transcript

00:01 Hi, i'm david and i'm here here here here i'm here here here here here here will be here here we're going to reveal about the common interval for the proportion let me remind you that the complement table for the proportion it will be the point estimate b heart plus and minus the margin of the error where the merchant of the error it will equal to the z and 4 over 2 time with the square root on the b heart times 1 minus b heart the value b n in this question here we need to find the sum of size needed to have the margin of the error equal to the 0 .04.

00:43 And with the 99 .51%, and the 99 .51%, we have the n -5 equal to the 100 % minus 99 .51%.

00:58 It will equal to the 0 .49%, which is equal to the 0 .409%, which is equal to the 0 .409%.

01:10 And then we need to find the z unfound over 2 so unfound over 2 it will equal to the 0 0245 and you need to find this critical value i need to bring up the z table so let me copy the z table and i put it on the right here now we have to look for the value of the z 0245 and we have to look for the value of the zpon 0245 and we we see the 2 4, 5, it will be average between the two values here.

01:49 And then it will be the g -com, the minus 2 .815.

01:57 So the critical value will be positive value, so we turn the 2 .815.

02:04 And then from here we will be able to find the p -hatt, where we have the p -hut.

02:13 Equal to x over n x equal to the 118 and n equal to the 200 then we get equal to the 0 .59 so from here we will have applied the formula for the margin of the error margin of the error equals to the 0 .04 and by the formula equal to the zan4 over 2 then with the square root under 0 .59 times 1...

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