# How to find margin of error & confidence interval on TI-83 in this problem?

I've found both of those things before on the calculator but I was given additional information in the problem. I'm just trying to figure out how to calculate those two figures with the calculator in this particular problem (since my online math class doesn't provide instructions for calculators):

Assume you plan to construct a 95% confidence interval.

Number of applications in sample:

In 2003: 42 Current Year: 33

Number of online applications in sample:

In 2003: 14 Current Year: 18

I'm thinking it's supposed to be set up like an n1, x1, n2, x2 type problem but when I used the 2PropZtest it didn't give the margin of error.

Would anyone happen to know how to calculate the margin of error and the 95% confidence interval? I know the answers because of my class's walkthrough, but it doesn't describe how to arrive at the answers on a calculator, it just says "use technology."

Any help is appreciated, thanks!!

### 3 Answers

- 8 years agoFavorite Answer
I had the same question and just found the answer, so I thought I'd share.

Do the 2PropZInt (scroll down below 2PropZTest). Then, you take the upper confidence level limit and subtract the lower confidence level limit. Then, divide by 2.

- JoAnnLv 44 years ago
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c) The way my stats teacher taught us to calculate the margin of error was: ME = z* x SE(x) I found the z* using invNorm(.025) on my calculator (a TI-83), however you might do it some other way. Then SE, or standard error, is your standard deviation divided by the square root of your sample size. So, 16.16 / √5 = 7.2250. Substitute these values and you have your answer. ME = z* x SE(x) ME = 1.96 x 7.2250 ME = 14.1609 However, if you have learned about the t model, it would be smarter to use this since your sample size of 5 is so small. If not, ignore this part. In this case, you would have to find t* which is invT on a calculator, or you can use a table to get the value of 2.776. It would be solved almost exactly the same after this. ME = z* x SE(x) ME = 2.776 x 7.2250 ME = 20.0565 d) A confidence interval is found using the following equation: x ± (ME) where x is 75. If you used the z*, you would get a value of 60.8391 to 89.1609. If you used the t*, you would get a value of 54.9435 to 95.0565. Hope this helps!