## StClowers Group Title In order to estimate the mean amount of time computer users spend on the internet each month, how many computer users must be surveyed in order to be 95% confident that your sample mean is within 15 minutes of the population mean? Assume that the standard deviation of the population of monthly time spent on the internet is 192 min. The minimum sample size required is ___ computer users. What is a major obstacle to getting a good estimate of the population mean? a. The data does not provide information on what the computer users did while on the internet. b. There may not be 630 computer users to survey c. It is difficult to precisely measure the amount of time spent on the internet, invalidating some data values. d. There are no obstacles to getting a good estimate of the population mean. 6 months ago 6 months ago

1. mathmale Group Title

This topic is closely related to confidence intervals and uses most or all of the same parameters (variables). Pls bring me up to date: What type of references do you have available? Do you have a textbook, a list of statistics formulas, skill in looking things up on the 'Net, or ... ?

2. mathmale Group Title

This web site is a bit too advanced, but does present the formula you need for minimum sample size: http://www.itl.nist.gov/div898/handbook/prc/section2/prc222.htm About 3/4 of the way from the top of the first page, there's a formula that begins with N. That's the one we need to consider here.

3. StClowers Group Title

I have a Ti84 calc.....

4. StClowers Group Title

I see several formulas that begin with N lol

5. StClowers Group Title

@mathmale ...will the formula be N$\ge \left(\begin{matrix}15 \\ 192\end{matrix}\right)^{2}\delta ^{2}$

6. StClowers Group Title

I dunno how to solve it though...can you tell me which number goes where

7. mathmale Group Title

Glad you're at least trying something. If y ou'll look at the formula in that web site again, you'll see several quantities: 1.96 is called the z-critical value and is connected with a 95% confidence interval; the quantity in the denominator is the tolerance (which in this problem is 15 min) and that sigma is the std. deviation. I'd like to take a lot more time to explain this in more depth, but it does appear to me that you have all the info you need to calculate N.

8. StClowers Group Title

im trying to enter it in my Ti84 and not sure how to do it...

9. StClowers Group Title

@mathmale

10. mathmale Group Title

$(\frac{ 1.96 }{ 15 })^{2}(192)^{2}$ is waht y ou want to calculate. Are you comfortable using parentheses on your calculator?

11. StClowers Group Title

yes i think so...i will find out lol

12. StClowers Group Title

so I got 2.27 Is that right?

13. mathmale Group Title

I haven't actually done it myself, but if you wouldn't mind, I'm going to lead you thru this calculation again. Type this into your calc.: (1.96/15) (in precisely that order) and then press the 2 x key on the left side of your calculato0r keyboard. What do you get?

14. mathmale Group Title

Note that the 2 x key, when pressed, will square the quantity within parentheses for you after you've pressed the ENTER key.

15. StClowers Group Title

when i typed that in, I typed 2 then the 2x key and it put 2^2, is that right?

16. StClowers Group Title

nevermind, got it...lol i got .0170737778

17. mathmale Group Title

sorry, i didn't see what y ou'd typed and was waiting. Plese clear the calculator.

18. mathmale Group Title

Type in ( 1.96 / 15 ) x^2 and ENTER in that order. you should obtain 0.01707.

19. StClowers Group Title

did you see what i got...i think we typed at the same time....

20. StClowers Group Title

yes i got that same answer

21. mathmale Group Title

Ooops. Do you have 0.017... still displayed? if so, pls don't erase it.

22. StClowers Group Title

yes i do

23. StClowers Group Title

so then i would type (192)^2 ?

24. mathmale Group Title

Great. Now we're going to do the last part of the calculation. keeping that 0.01707 as it is, type in the following: 2 x 192 x ENTER in that order. The first x stands for multiplication and is a key by itself on the right side of your calc, and the 2 x is the same command key you used earllier.

25. mathmale Group Title

I got the result 141616.7, which I rounded up to 141617.

26. StClowers Group Title

i got 629.407 ...?!?!

27. mathmale Group Title

Let me check my own work. Actually, your result looks more reasonable than does mine!!

28. mathmale Group Title

How extremely embarrassing. You're right; I'm wrong. You must now round up (not down) to the nearest integer number N. What's your N?

29. StClowers Group Title

my N is 629.408 ? is that right? or maybe 629.41

30. StClowers Group Title

oh wait....actually that would be 629

31. StClowers Group Title

since its asking for number of computer users

32. mathmale Group Title

What I meant was that you must eliminate all decimal fractions in your result by rounding up appropriately. 629.4077 has that decimal fraction 0.4077, which we do NOT want. MUST roud up to the nearest integer. Try again.

33. StClowers Group Title

629

34. mathmale Group Title

Obviously we don't want to see 0.4077 computer user. Bloody. :)

35. StClowers Group Title

LOL

36. mathmale Group Title

You've rounded down. We MUST round UP to be conservative in our estimate.

37. mathmale Group Title

round 629.4077 UP to the nearest integer.

38. StClowers Group Title

oh yeah...sorry bout that....it would be 630?

39. mathmale Group Title

Right. Perfect. You went beyond what the question asked you for; you have enuf data to choose the fourth possible answer as the correct answer, and you went thru the actual calculations to find N=630, the number of computer users you must survey (poll) in order to be no more than 15 min off the true population mean of the total time the pop of computer users spends on the Internet/month.

40. mathmale Group Title

Very, very good. Thanks for your persistence and positive attitude.

41. StClowers Group Title

Thank you so much!!! You are the best helper on here indeed...its so true...not many take these steps and time to explain. :)

42. mathmale Group Title

While this in itself is not sufficient practice, you've made huge, positive strides towards learning this material!

43. mathmale Group Title

thank you! I've been on the Internet nearly 12 hours today, so need to log off; I urge you to post each new part of this same problem and see if someone can help you. I may be on the 'Net tomorrow (but probably not).

44. StClowers Group Title

ok thank you so much!

45. mathmale Group Title

Great pleasure! Bye.

46. StClowers Group Title

gnight