SOLUTION: A sample of 20 pages was taken without replacement from the 1,591-page phone directory Ameritech Pages Plus Yellow Pages. On each page, the mean area devoted to display ads was mea

Algebra ->  Probability-and-statistics -> SOLUTION: A sample of 20 pages was taken without replacement from the 1,591-page phone directory Ameritech Pages Plus Yellow Pages. On each page, the mean area devoted to display ads was mea      Log On


   

Question 173497: A sample of 20 pages was taken without replacement from the 1,591-page phone directory Ameritech Pages Plus Yellow Pages. On each page, the mean area devoted to display ads was measured (a display ad is a large block of multicolored illustrations, maps, and text). The data (in square millimeters) are shown below:
0
260
356
403
536
0
268
369
428
536

268
396
469
536
162
338
403
536
536
130
(a) Construct a 95 percent confidence interval for the true mean.b) Why might normality be an issue here?(c) What sample size would be needed to obtain an error of ±10 square millimeters with 99 percent confidence? (d) If this is not a reasonable requirement, suggest one that is.

Answer by Edwin McCravy(20086) About Me  (Show Source):
You can put this solution on YOUR website!

(a) Construct a 95 percent confidence interval for the true mean.

On your TI-83 or 84 calculator

Press STAT then ENTER

Put all 20 numbers in L1

Press STAT, press right arrow once to highlight CALC
Press ENTER twice.

You'll see some statistics come up on the screen

Press STAT then the right arrow twice to highlight TESTS
Then press 8 to get T-Interval

You see the TInterval menu.
Make sure Stats is highlighted

You should see:

TInterval
 Inpt:Data Stats
 x:346.5
 Sx:170.3783714...
 n:20
 C-Level:.95
 Calculate

Type .95 after C-Level if it's not there

Scroll down to highlight "Calculate"

Press ENTER

You should see 
TInterval
(266.76,426.24)
x=346.5
Sx=170.3783715
n=20

That's your confidence interval

(266.76,426.24)

or maybe your book writes it as 

266.76+%3C+x+%3C+426.24

--------------

.b) Why might normality be an issue here?

Because it is a small sample and we must assume
that the data be nomally distributed.

--------------

(c) What sample size would be needed to obtain an error of ±10 square millimeters with 99 percent confidence? 

We use the formula:



First we find matrix%282%2C1%2Cz%5Balpha%2F2%5D%2C%22%22%29

Subtract .99 from 1, getting .01, then divide this by 2
to get .005 

Press 2nd then VARS to get the DISTR menu
Press 3 to get invNorm( on the main screen

then after InvNorm(, type .005 and close the
parentheses, so that you see

InvNorm(.005)

on the main screen.

Press ENTER and you read -2.575829303

Now substitute in the formula:





Get 1926.030165

Round UP to 1927, (even though you were told in 
elementary school to round down when the first
digit dropped is less than 5) 
---------------

(d) If this is not a reasonable requirement, 

This is not reasonable because there are only 1591 pages
in the directory.

suggest one that is.

Reduce the confidence level requirement to 90%.

Do the above using .9 instead of .99 and get
that the sample size needed is 786, which is not
unreasonable.

Edwin