Question 173497

(a) Construct a 95 percent confidence interval for the true mean.
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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
 <u>I</u>npt: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 < x < 426.24}}}

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.b) Why might normality be an issue here?
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Because it is a small sample and we must assume
that the data be nomally distributed.

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

{{{n=(matrix(4,1,z[alpha/2]*sigma,"",
            "----------",
              E))^2}}}

First we find {{{matrix(2,1,z[alpha/2],"")}}}

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:

{{{n=(matrix(4,1,z[alpha/2]*sigma,"",
            "----------",
              E))^2}}}

{{{n=(matrix(3,1,-2.575829303*170.3783715,
            "----------------------",
              10))^2}}}

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) 
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(d) If this is not a reasonable requirement, 
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This is not reasonable because there are only 1591 pages
in the directory.
</pre></font></b>
suggest one that is.
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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</pre>