Question

Use the following information to answer the next five exercises. A study was conducted to test the effectiveness of a software patch in reducing system failures over a six-month period. Results for randomly selected installations are shown in Table 10.21. The “before” value is matched to an “after” value, and the differences are calculated. The differences have a normal distribution. Test at the 1% significance level.

What is the p-value?

Short answer

The required p-value is $0.00669$.

Step-by-step solution

Given information

The given table is

Find the value of p?

Test using TI-83+calculator applying the steps below:

Step 1: To run the Setup Editor command, press STAT followed by 5 and then ENTER.

Step 2: To open the Stat List editor, press STAT followed by 1.

Step 3: Go to the name in the third list and enter the list for before and after values. Then enter ${\mathrm{L}}_2-{\mathrm{L}}_1$then press ENTER after each value. The data is:

Step 4: Again press STAT and then the arrow $(\to )$to TESTS.

Step 5: Next press the arrow $(\downarrow )$to 2 : T-Test then press enter.

Step 6: Use the arrow $(\to )$to DATA and again press enter.

Step 7: Finally press the arrow (?) and enter the inputs :

Step 8: Lastly press the arrow (?) to calculator and press enter key. The output is:

The p-value is $0.00669$