anonymous
  • anonymous
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.
Mathematics
katieb
  • katieb
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anonymous
  • anonymous
anonymous
  • anonymous
I don't know how to even start this D:
batman19991
  • 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
  • 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
  • batman19991
"Margin of Error" is 6% and your welcome
anonymous
  • 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
  • batman19991
idk sorry
jim_thompson5910
  • 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
  • anonymous
OHHHHH
anonymous
  • anonymous
so in the formula\[1.96 * \sqrt{\frac{ p(1 - p) }{ n }}\] p would be "0.7", right?
anonymous
  • anonymous
in my class they taught me "p" is proportion and "n" is sample size
anonymous
  • anonymous
oh wait it would be "1.645" instead of "1.96" I think, because it's a 90% confidence interval, right?
jim_thompson5910
  • jim_thompson5910
we weren't given the sample size though
anonymous
  • 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
  • batman19991
oh well sorry dude
anonymous
  • anonymous
maybe the first time is the percentage "90%" and the second time is the "66% - 74%' range that you calculated?
jim_thompson5910
  • jim_thompson5910
or you can say (0.66, 0.74)
anonymous
  • 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
  • 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
  • anonymous
Oh okay! That sounds great!! Thank you so much!
jim_thompson5910
  • jim_thompson5910
"this means that 66% - 77% of the seniors" that's an incorrect way to state it
anonymous
  • anonymous
Sorry! I meant 66% - 74%. It was a typo lol
jim_thompson5910
  • jim_thompson5910
the proportions we're dealing with aren't proportions of the population size they are test scores
anonymous
  • 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
  • jim_thompson5910
that's also incorrect
anonymous
  • anonymous
would it be 66% - 74% of the time, the seniors will have an average test score?
anonymous
  • anonymous
wait so the population proportion is somewhere between "66% - 74%"
jim_thompson5910
  • 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
  • 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
  • jim_thompson5910
you're welcome

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