Hypothesis Tests and Confidence Intervals

The position of the graphically represented keys can be found by moving your mouse on top of the graphic. 
The row of function keys: f1, f2, etc. do not count as a row. Row 1 starts with the blue 2nd key.

Entering data

Press The Apps Key: Row 2, Column 3, then arrow over to the Stats/List Editor. (It should be 3 down arrows and two right arrows.) Press The Enter Key: Row 9, Column 5 The Enter Key: Row 9, Column 5.  Now follow the instructions below.
one variable
Enter the x-values one by one, pressing The Enter Key: Row 9, Column 5 after each one.
two variables
Enter the x-values one by one, pressing The Enter Key: Row 9, Column 5 after each one. Press The Right Arrow - Above Right near the top row. to get to the second column. Enter the y-values one by one, pressing The Enter Key: Row 9, Column 5 after each one. 

 

Running hypothesis tests
The problem is to test the hypothesis - H0: m = m0We are doing a double sided test. Assume the standard deviation iss
Z-Test
  1. Press The Second Key: Row 1, Column 1 It's light blue. The f1 Key: Top Row, first on the left (The F6 menu should drop).
  2. Now press The One Key: Row 8, Column 2 for Z-Test.... 
  3. Press The Enter Key: Row 9, Column 5 to accept Data input method as Data. 
  4. Enter m0 and press The Down Arrow - Above Right.
  5. Enter s and press The Down Arrow - Above Right. 
  6. Enter list1 in the List: area. You only have to do this once. The calculator will remember it for future calculations.
  7. Press The Down Arrow - Above Right to accept 1 as Freq. 
  8. Press if you wish to choose a different hypothesis test. Arrow to your choice and press The Enter Key: Row 9, Column 5. (Choices are m ≠ m0, m < m0, and m > m0.)
  9. Press The Enter Key: Row 9, Column 5 to signal OK.  A list in a new window will appear. The z-value appears in the second entry. The P Value appears in the third. See the below example for interpretation.
T-Test
Exactly as above, except press The Two Key: Row 8, Column 3 for T-Test... (step 2) instead of The One Key: Row 8, Column 2.

Computing confidence intervals
Z Interval
  1. Press The Second Key: Row 1, Column 1 It's light blue. The f2 Key: Top Row, second from the left (The F7 menu should drop).
  2. Now press The One Key: Row 8, Column 2 for ZInterval.... 
  3. Press The Enter Key: Row 9, Column 5 to accept Data input method as Data.
  4. Enter s and press The Down Arrow - Above Right.
  5. Enter list1 in the List: area. You only have to do this once. The calculator will remember it for future calculations.
  6. Press The Down Arrow - Above Right to accept 1 as Freq.
  7. Enter a C Level (that is, confidence level. This will generally be .95 or .99.) Press The Enter Key: Row 9, Column 5 to signal OK.
  8. A list in a new window will appear. The confidence level is the first entry.
T Interval
  1. Press The Second Key: Row 1, Column 1 It's light blue. The f2 Key: Top Row, second from the left (The F7 menu should drop).
  2. Now press The Two Key: Row 8, Column 3 for TInterval....
  3. Press The Enter Key: Row 9, Column 5 to accept Data input method as Data.
  4. Enter list1 in the List: area. You only have to do this once. The calculator will remember it for future calculations.
  5. Press The Down Arrow - Above Right to accept 1 as Freq.
  6. Enter a C Level (that is, confidence level. This will generally be .95 or .99.) Press The Enter Key: Row 9, Column 5 Press The Enter Key: Row 9, Column 5 again to signal OK. (If the correct C Level is already there, you only need to press The Enter Key: Row 9, Column 5 once.
  7. A list in a new window will appear. The confidence level is the first entry.

 

Worked Out Examples

In the following examples, we list the exact key sequence used to find the answer.  We will list the keys by the main symbol on the key.  In parentheses, we will list a helpful mnemonic, e.g. we will list ex as (ex).

Run a Z-test on this list of numbers to test the hypothesis that m = 88. Assume that s = 2.7.

87 89 91 93 88 90 94 92 92 85
Solution:

The Second Key: Row 1, Column 1 It's light blue. The f1 Key: Top Row, first on the left (F6 menu) The One Key: Row 8, Column 2 (Z-Test...) The Enter Key: Row 9, Column 5 (Data) The Eight Key: Row 6, Column 3 The Eight Key: Row 6, Column 3 (m0) The Down Arrow - Above Right The Two Key: Row 8, Column 3 The Decimal Point Key: Row 9, Column 3 The Seven Key: Row 6, Column 2 (s) The Down Arrow - Above Right list1, (if necessary)The Down Arrow - Above Right The Down Arrow - Above Right The Down Arrow - Above Right (to accept the two sided test) The Enter Key: Row 9, Column 5  

You should get a z value of 2.45954929 and a P Value of .013911171. Because P < 0.05, we reject the null hypothesis and conclude that the mean is not 88.

Run a T-test on this list of numbers to test the hypothesis that m=54.

51 60 54 57 54 55 59 52 52 58
Solution:

The Second Key: Row 1, Column 1 It's light blue. The f1 Key: Top Row, first on the left (F6 menu) The Two Key: Row 8, Column 3 (T-Test...) The Enter Key: Row 9, Column 5 (Data) The Five Key: Row 7, Column 3 The Four Key: Row 7, Column 2 (m0) The Down Arrow - Above Right list1, (if necessary)The Down Arrow - Above Right The Down Arrow - Above Right The Down Arrow - Above Right (to accept the two sided test) The Enter Key: Row 9, Column 5  

You should get a t-value of 1.20267559 and a P Value of 0.259786095. Since P > 0.05, we cannot conclude that m does not equal 54.

Find a 99% z-confidence interval for the row of numbers. Assume s is 2.7. 

87 89 91 93 88 90 94 92 92 85
Solution:

  The Second Key: Row 1, Column 1 It's light blue. The f2 Key: Top Row, second from the left (F7 menu) The One Key: Row 8, Column 2 (ZInterval...) The Enter Key: Row 9, Column 5 (Data) The Two Key: Row 8, Column 3 The Decimal Point Key: Row 9, Column 3 The Seven Key: Row 6, Column 2 (s) The Down Arrow - Above Right list1 (if necessary) The Down Arrow - Above Right The Decimal Point Key: Row 9, Column 3 The Nine Key: Row 6, Column 4 The Nine Key: Row 6, Column 4 The Enter Key: Row 9, Column 5 The Enter Key: Row 9, Column 5

 You should get a confidence interval of {87.9,92.3}.

Find a 95% t-confidence interval for the row of numbers.

3 1 4 1 5 9 2 6 5 3
Solution:

 The Second Key: Row 1, Column 1 It's light blue. The f2 Key: Top Row, second from the left (F7 menu) The Two Key: Row 8, Column 3 (TInterval...) The Enter Key: Row 9, Column 5 (Data) list1 (if necessary) The Down Arrow - Above Right The Decimal Point Key: Row 9, Column 3 The Nine Key: Row 6, Column 4 The Nine Key: Row 6, Column 4 The Enter Key: Row 9, Column 5 The Enter Key: Row 9, Column 5

You should get a confidence interval of {2.133, 5.667}.

 

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