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Computing the P-Value of a Right-Tailed Test

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

Enter the data from Table 1 on pg. 532 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 2^nd [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 2^nd [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.)

The hypothesis test,    vs. , is a right-tailed test.  The population standard deviation,  , is 3500.  The Z-Test is the appropriate test.  To run the test, press STAT, highlight TESTS and select 1:Z-Test.  Since you are using the actual data, which is stored in L1, for the analysis, select Data for Inpt and press ENTER.  For    enter 10300, the value for  in the null hypothesis.  For  enter 3500.  Enter L1 for List, and 1 for Freq.  On the next line, choose the appropriate alternative hypothesis and press ENTER.  For this example, it is , a right –tailed test.

There are two choices for the output of this test.  The first choice is Calculate.  The output displays the alternative hypotheses, the calculated z-value, the P-value, and n.

Since p=.0045, which is less than a, the correct conclusion is to Reject  .

To view the second output option, press STAT, highlight TESTS, and select 1:Z-Test.  All the necessary information for this example is still stored in the calculator.  Scroll down to the bottom line and select DRAW.  A normal curve is displayed with the right-tail area of .0045 shaded.  (Note:  Because the area is so small in this example, it is not really visible in the curve.)  This shaded area is the area to the right of the calculated Z-value.  The Z-value and the P-value are also displayed.