Question

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.

Answer 1

@maha2458
@batman19991

Answer 2

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

Answer 3

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

Answer 4

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

Answer 5

"Margin of Error" is 6% and your welcome

Answer 6

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?

Answer 7

idk sorry

Answer 8

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%)

Answer 9

OHHHHH

Answer 10

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

Answer 11

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

Answer 12

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

Answer 13

we weren't given the sample size though

Answer 14

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 ._.

Answer 15

oh well sorry dude

Answer 16

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

Answer 17

or you can say (0.66, 0.74)

Answer 18

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.

Answer 19

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)

Answer 20

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

Answer 21

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

Answer 22

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

Answer 23

the proportions we're dealing with aren't proportions of the population size

they are test scores

Answer 24

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."

Answer 25

that's also incorrect

Answer 26

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

Answer 27

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

Answer 28

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

Answer 29

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.

Answer 30

you're welcome