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Calculating P-values for a T-Test

 

Example: Using the data from Example 1 in your text book, test the nutritionist’s claim, using the P-value approach at the  level of significance.

 

Enter the data from Table 3 on pg. 548 into L1.  Because the sample size is less than 30, the data must be tested for normality and checked for outliers.

 

To set up the normal probability plot, press 2nd [STAT PLOT] .  Press ENTER to select Plot 1.  Highlight On and press ENTER.  Set Type to the normal probability plot which is the third selection in the second row.  Press ENTER.  Set Data List to L1 and Data Axis to X.  For Marks select the small square.

 

Press ZOOM and select 9:ZoomStat and ENTER.

 

 

 

This plot is fairly linear, indicating that the data generally follows a normal distribution.

 

To set up the boxplot, press 2nd [STAT PLOT].  Press ENTER to select Plot 1.  Highlight On and press ENTER.  Set Type to the boxplot with outliers which is the first selection in the second row.  Press ENTER.  Set XList to L1 and Freq to 1.  For Marks select the small square.

 

Press ZOOM and select 9:ZoomStat and ENTER.

 

 

There are no outliers indicated in the boxplot.  (Note:  Outliers would appear as *’s at the extreme left or right ends of the boxplot.)

 

This test is a right-tailed test of   vs.     Since n < 30 , and the population standard deviation, , is unknown, the T-Test is the appropriate test.  This test requires the underlying population to be approximately normally distributed with no outliers, as was verified in the plots.

 

Press STAT, highlight TESTS and select 2:T-Test.  Choose Data for Inpt and press ENTER.  Fill in the following information:   = 142.8, List = L1, and Freq=1.  Choose the right-tailed alternative hypothesis,  , and press ENTER.  Highlight Calculate and press ENTER.

 

 

Or, highlight Draw and press ENTER.

 

 

Since the P-value is greater than a, the correct conclusion is to Fail to Reject .