For this problem carry at least four digits after the...

For this problem, carry at least four digits after the decimal in your calculations. Answers may vary slightly due to rounding. What percentage of your campus student body is female? Let p be the proportion of women students on your campus. (a) If no preliminary study is made to estimate p, how large a sample is needed to be 99% sure that a point estimate p̂ will be within a distance of 0.07 from p? (Round your answer up to the nearest whole number.) students (b) A report indicates that approximately 63% of college students are females. Answer part (a) using this estimate for p. (Round your answer up to the nearest whole number.) students

Transcript

00:01 Hey there, welcome to numerate.

00:03 So we are looking at the percentage of campus student body, the percentage of being females.

00:11 So we're looking at the proportion of women's students on campus, basically.

00:15 For part a, we're trying to be 99 % confident that the population proportion would be a distance of 0 .07 from the proportion, given no prior estimate here.

00:28 So our equation that we're going to use for parts a and b will be the margin of error equation, and then we're going to manipulate it to solve for n.

00:42 So therefore, a margin of error equals z critical value, multiplied by the square root of a proportion times 1 minus our proportion divided by n.

01:02 So we're going to solve for n.

01:04 Therefore n will equal our proportion times one minus our proportion divided by our margin of error divided by the z critical value square so basically what we did first is to move the z critical value to the left side and then we're going to square both sides and we move n to the left and move the margin of error divided by the z critical value back to the right which is divided by dot square.

01:44 Okay.

01:45 This is how we got the manipulation equation here.

01:48 So let's plug in our values.

01:50 Since we are given no prior estimates here, our proportion will be 0 .5.

01:56 1 minus 0 .5 will be 0 .5.

01:59 So this will be divided by.

02:03 Our margin of error.

02:05 So our margin of error is given to us within a distance of 0 .0 .0.

02:12 7 divided by our z critical value.

02:21 So our z critical value is based off a 99 % confidence, given us a critical value of around 2 .58.

02:36 And this is going to be squared...