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TI-83 Plus Basics: Taking the Square Root of a Number

TI-83 Plus Basics: Taking the Square Root of a Number

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So suppose you are given the following formula and asked to find the z statistic for some set of data when the population proportion is 23%, the sample proportion is 160 over 540, and the number of samples is 540. How can we do this calculation on a TI-83 Plus?


z equals fraction numerator begin display style p with hat on top end style minus p over denominator square root of begin display style fraction numerator p q over denominator n end fraction end style end root end fraction


Always remember that you should not get caught up trying to enter the entire formula into the calculator, especially if you are not familiar with the functions or have a hard time keeping track of which operations will be performed first. Instead break the problem up into parts and then combine your parts once the remaining operations become simpler.

For example, in this problem, notice that what we have here is a really fancy looking fraction. The numerator of this fraction is simple enough (p with hat on top minus p), but the denominator (square root of fraction numerator p q over denominator n end fraction end root) is a little more complex. Our goal then will be to evaluate the numerator and denominator separately and then combine our results by dividing our final value for the numerator by the final value for the denominator.


Solving for the Numerator:

To solve for the numerator simply plug in the values of p with hat on top and subtract it by p. For this problem this should look like the following on your TI-83 Plus.


Source: Parmanand Jagnandan

Source: Parmanand Jagnandan via thinglink

Now hit ENTER and you should get a value of .0662962963. This value represents our numerator. Now let's calculate the denominator.

A word of note here before we move on, for most problems try to keep as many digits in your number as possible and then round at the very end of the problem. This will help most online automated answer checkers to correctly grade your answers.

Solving for the Denominator:

To solve for the denominator first we need to remember that if we know p, then q is going to given by 1 minus p. Since we know that the population proportion is 0.23, then q must equal 1 - 0.23, or 0.77. This means that when we enter in the denominator into the calculator we should have the following:



Source: Parmanand Jagnandan via thinglink

Next we hit ENTER and should get a value of 3.27962963E-4.

From here we can use the 2ndsquare root of blank end root, and ANS functions to help us find the value of the denominator. So how do we use these functions. First we press 2nd on the keypad then press the x squared, which because we pressed the 2nd button is now the square root function (square root of blank end root). Then we press the 2nd button again and then press ANS, which tells the calculator that we want to take the square root of the value it previously gave us, in this case we are taking the square root of 3.27962963E-4. Then use the parentheses button to close off the square root function, which tells the calculator to only take the square root of the previous answer. If you do this correctly, your screen should look like the following:

Source: Parmanand Jagnandan via thinglink

One thing to keep in mind here is that 3.27962963E-4 is the same as 0.000327962963.

Hitting ENTER you should get a value of .0181097477, which is the value of our denominator.

Putting it All Together

So now that we have our numerator (.0662962963) and denominator (.0181097477) we can simply divide the numerator by the denominator to get the value of our z statistic, which is 3.66 rounded to the hundredths place.


Solve the Problem All at Once

Once you get familiar with the functions of this calculator you can solve the entire problem all at once. To do so you would input the following. I leave it up to you to figure out the meaning from here.