A field test for a new exam was given to randomly selected seniors. The exams were graded, and the sample mean and sample standard deviation were calculated. Based on the results, the exam creator claims that on the same exam, nine times out of ten, seniors will have an average score within 4% of 70%.
Is the confidence interval at 90%, 95%, or 99%? What is the margin of error? Calculate the confidence interval and explain what it means in terms of the situation.

- anonymous

- katieb

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- anonymous

- anonymous

I don't know how to even start this D:

- batman19991

the exam creator claims that on the same exam, nine times out of ten, seniors will have an average score within 6% of 80%.
90% is 1.645, 95% is 1.96, 99% is 2.575
so 9 / 10 means 90 / 100
the Confidence Interval is 90% accurate,
i dont know if this helps though

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- anonymous

ohhhh okay! yes of course it does! because now I just need the margin of error and I'm done!!! thank you so much :)

- batman19991

"Margin of Error" is 6% and your welcome

- anonymous

oh okay! lol you mean "4%" ? my problem says "4% of 70%". I have no idea what the "of 70%' part means..what do you think it could mean? of 70% of the students?

- batman19991

idk sorry

- jim_thompson5910

it means that 70% is the estimate of the true population proportion
the 4% is the margin of error which allows some wiggle room. The true population proportion is probably not exactly 70%, but somewhere in the range from 66% to 74% (notice how I added and subtracted 4% from 70%)

- anonymous

OHHHHH

- anonymous

so in the formula\[1.96 * \sqrt{\frac{ p(1 - p) }{ n }}\]
p would be "0.7", right?

- anonymous

in my class they taught me "p" is proportion and "n" is sample size

- anonymous

oh wait
it would be "1.645" instead of "1.96" I think, because it's a 90% confidence interval, right?

- jim_thompson5910

we weren't given the sample size though

- anonymous

yeah that's what I found confusing :/ but the question only asks for the confidence interval, the margin of error, and the confidence interval....hm I wonder why it asks for the confidence interval twice ._.

- batman19991

oh well sorry dude

- anonymous

maybe the first time is the percentage "90%" and the second time is the "66% - 74%' range that you calculated?

- jim_thompson5910

or you can say (0.66, 0.74)

- anonymous

How is this?
The confidence interval is 90% because the exam claims that nine times out of ten, the seniors will have an average score within 4% of 70%.
The margin of error is 4%.
The proportion would be 70%, meaning that the confidence interval is between 66% and 74%.
In terms of the situation, this means that 66% - 77% of the seniors will have an average score, 90% of the time.

- jim_thompson5910

The sample proportion would be 70%
The population proportion is what we're after. It is unknown, but very likely to be somewhere between 66% and 74% (with 90% confidence)

- anonymous

Oh okay! That sounds great!! Thank you so much!

- jim_thompson5910

"this means that 66% - 77% of the seniors" that's an incorrect way to state it

- anonymous

Sorry! I meant 66% - 74%. It was a typo lol

- jim_thompson5910

the proportions we're dealing with aren't proportions of the population size
they are test scores

- anonymous

Oh so should I write "In terms of the situation, this means that 66% - 74% of the time, the test scores will be average, with 90% confidence."

- jim_thompson5910

that's also incorrect

- anonymous

would it be 66% - 74% of the time, the seniors will have an average test score?

- anonymous

wait so the population proportion is somewhere between "66% - 74%"

- jim_thompson5910

Here's what is going on
The teacher gathered up a sample of students. Say n = 100. We weren't given this value of n, but let's say it's 100. The teacher tested the students and then found the sample mean to be 0.70
This sample mean is the average test score of just the sample. The actual population mean is unknown
The teacher claims that the true population mean is somewhere between 0.66 and 0.74, again those two numbers are test scores. So the true population mean of the test scores could be 0.71 or 0.68. We don't know for sure since we're not 100% confident. The 90% confidence means there is some room for error and the true population mean could be outside of this range

- anonymous

Ohhhh!!! I understand now. I think I was getting confused with "population mean" and "sample mean". Thank you so much. You truly are a life saver.

- jim_thompson5910

you're welcome

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