History Bookmarks Window Help 83 @ mathxl.com INSS220 MWF 10AM_Fall2017 Devin Bu

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History Bookmarks Window Help 83 @ mathxl.com INSS220 MWF 10AM_Fall2017 Devin Burke 11/3/17 12:51 PM Test: Exam 2 Time Remaining: 0026:08 Submit Te This Question: 6 pts | 25 of 25 022 complete) This Test: 100 pts poss Determine the sample size needed to construct a 99% conf ence interval to estimate e vera e GPA for the student population et a colege with a margin of error equal to 0.4. Assume the standard deviation of the GPA for the student population is 1.0. The sample size needed is Round up to the nearest integer) Enter your anawer in the answer box.

Explanation / Answer

As we know that the formula for the normual distribution is

margin of error= z*sd/Sqrt(n)

where we have been given sd=1margin of error =0.4 and we need to determine n i.e. sample size

Now putting the values in the above equation we get

0.4=z*1/sqrt(n)

so., sqrt(n)=z/0.4

so n= (z*z)/0.16

now we need the find the z value at 99% conf level while it's a two tail test.

so., the value from the z table is +/- 2.575829 while to calculate n we need to take z^2 in to consideration which makes signs irrelavent

So., n= 2.575829 *2.575829 /6=6.634895/0.16 = 41.46809

And so by rounding the number to the nearest integer, we can say that n=41 should be the sample size.

PS: hope this has helped you in understanding the problem. Pls upvote the ans if it has really helped you. Good Luck!!

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