Hello!
Is this the entire problem/question? Do you know the mean of ages of seniors at OP College?
Confidence interval means that we can state we are 80% confident that the mean ages of seniors at OP College is between x and y. We need to find those numbers.
The general steps of finding a confidence interval for a sample are: Since it's sample data, we are using a t value, if it were population data we would use z.
Confidence interval formula mean +/- t (s / √n) It may be represented by an E in your book, margin of error
1) Find t value. You need alpha and degrees of freedom (df) to do this. Alpha = 100% - (confidence interval) for both tails, divide by 2 to get one tail.
df = n - 1
In this case, alpha = ∝ = 100 - 80 = 20 / 2 = 10% or 0.1 and df = 30 -1 = 29.
Then use your calculator or table to find the t value. On TI84, 2nd VARS invNorm
2) Find standard error. SE = sample mean / (√sample size) or SE = ∂ / (√n)
In this case, SE = 2.6 / (√30)
3) Multiple t value and standard error. This is the number you will add to your mean and subtract from your mean to get the confidence interval.
4) Find the confidence interval, add and subtract the number from 3.
sample mean - E < mean < sample mean + E
Let's say our E value is 0.62. I'm going to pretend the mean ages of seniors is 17.8 (because I don't know from the problem.
Then the confidence interval would be 17.8 - 0.62 < mean < 17.8 + 0.62
17.18 < mean < 18.42
So we can say that we are 80% confident that the TRUE population mean of seniors is between 17.18 and 18.42. Because we didn't ask every senior, so we are making an educated guess.
With confidence intervals, the more confident you are the bigger your interval is going to be. The less confidence you are, the smaller the interval. For example, I am 95% confident that your height is between 5"0 and 6"0. (I'm 95 % confident that you are 5 foot something. Pretty confident because that is a big range. I am 20% confident that your height is between 5"4 and 5"6. Not as confident because I don't know how tall you are. Make sense?
I hope this helps, let me know if you have any questions.
Margaret
