6.2 Calculating the p-value

To calculate the p-value you must modify the z-score table to highlight the area right of z, instead of the area left of z. The area left of z and the area right of z add up to 100% (confidence level). In order to calculate the area right of z, you simply need to subtract the area left of z from 100%. You can perform this calculation using Excel, as described in the following steps.

Step 1: Set up a new table with the exact layout of the previous z-score table used in Activity 5.

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Figure 26 Creating ‘Area right of z’ table step 1

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A picture of an ‘Area left to z’ table on the top and an ‘Area right to z’ table below with rows (labelled: 0.0; 0.1; 0.2; 0.3; 0.4; 0.5) and columns (labelled: 0.00; 0.01; 0.02; 0.03; 0.04, 0.05; 0.06; 0.07; 0.08; 0.09).

The ‘Area left to z’ table is filled out as follows:

Z Score	0.00	0.01	0.02	0.03	0.04	0.05	0.06	0.07	0.08	0.09
0.0	0.5000	0.5040	0.5080	0.5120	0.5160	0.5199	0.5239	0.5279	0.5319	0.5359
0.1	0.5398	0.5438	0.5478	0.05517	0.5557	0.5596	0.5636	0.5675	0.5714	0.5753
0.2	0.5793	0.5832	0.5871	0.5910	0.5948	0.5987	0.6026	0.6064	0.6103	0.6141
0.3	0.6179	0.6217	0.6255	0.6293	0.6331	0.6368	0.6406	0.6443	0.6480	0.6517
0.4	0.6554	0.6591	0.6628	0.6664	0.6700	0.6736	0.6772	0.6808	0.6844	0.6879
0.5	0.6915	0.6950	0.6985	0.7019	0.7054	0.7088	0.7123	0.7157	0.7190	0.7224

Figure 26 Creating ‘Area right of z’ table step 1

Step 2: Use the Excel function to calculate the values: the z-score in the ‘Area right of z’ table equals 1 minus the corresponding z-score in ‘Area left of z’ table.

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Figure 27 Creating ‘Area right of z’ table step 2

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In the image above, we have an ‘Area left to z’ table on the top and an ‘Area right to z’ table below with the equation 1 minus values from the area left to z table.

The ‘Area left to z’ table is filled out as follows:

Z Score	0.00	0.01	0.02	0.03	0.04	0.05	0.06	0.07	0.08	0.09
0.0	0.5000	0.5040	0.5080	0.5120	0.5160	0.5199	0.5239	0.5279	0.5319	0.5359
0.1	0.5398	0.5438	0.5478	0.05517	0.5557	0.5596	0.5636	0.5675	0.5714	0.5753
0.2	0.5793	0.5832	0.5871	0.5910	0.5948	0.5987	0.6026	0.6064	0.6103	0.6141
0.3	0.6179	0.6217	0.6255	0.6293	0.6331	0.6368	0.6406	0.6443	0.6480	0.6517
0.4	0.6554	0.6591	0.6628	0.6664	0.6700	0.6736	0.6772	0.6808	0.6844	0.6879
0.5	0.6915	0.6950	0.6985	0.7019	0.7054	0.7088	0.7123	0.7157	0.7190	0.7224

The formula ‘=1-B4’ appears in the ‘Area right to z’ table in the cell for row 0.0, column 0.00.

Figure 27 Creating ‘Area right of z’ table step 2

Step 3: Apply this calculation to all the cells in the Excel sheet.

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Figure 28 Creating ‘Area right of z’ table step 3

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In the image above, we have an ‘Area left to z’ table on the top and an ‘Area right to z’ table below.

The ‘Area left to z’ table is filled out as follows:

Z Score	0.00	0.01	0.02	0.03	0.04	0.05	0.06	0.07	0.08	0.09
0.0	0.5000	0.5040	0.5080	0.5120	0.5160	0.5199	0.5239	0.5279	0.5319	0.5359
0.1	0.5398	0.5438	0.5478	0.05517	0.5557	0.5596	0.5636	0.5675	0.5714	0.5753
0.2	0.5793	0.5832	0.5871	0.5910	0.5948	0.5987	0.6026	0.6064	0.6103	0.6141
0.3	0.6179	0.6217	0.6255	0.6293	0.6331	0.6368	0.6406	0.6443	0.6480	0.6517
0.4	0.6554	0.6591	0.6628	0.6664	0.6700	0.6736	0.6772	0.6808	0.6844	0.6879
0.5	0.6915	0.6950	0.6985	0.7019	0.7054	0.7088	0.7123	0.7157	0.7190	0.7224

The ‘Area right to z’ is completed as follows:

Z	0	0.01	0.02	0.03	0.04	0.05	0.06	0.07	0.08	0.09
0	0.5000	0.4960	0.4920	0.4880	0.4840	0.4801	0.4761	0.4721	0.4681	0.4641
0.1	0.4602	0.4562	0.4522	0.4483	0.4443	0.4404	0.4364	0.4325	0.4286	0.4247
0.2	0.4207	0.4168	0.4129	0.4090	0.4052	0.4013	0.3936	0.8936	0.3897	0.3859
0.3	0.3821	0.3783	0.3745	0.3707	0.3669	0.3632	0.3594	0.3557	0.3520	0.3483
0.4	0.3446	0.3409	0.3372	0.3336	0.3300	0.3264	0.3228	0.3192	0.3156	0.3121
0.5	0.3085	0.3050	0.3015	0.2981	0.2946	0.2912	0.2877	0.2843	0.2810	0.2776

Figure 28 Creating ‘Area right of z’ table step 3

Using these steps and the z-score table (Figure 28) that highlights the area left of z, you can create a new z-score table to highlight the area right of z..

Using Table 5, you can determine an exact p-value for the sample mean. In order to illustrate this point, try to solve the problems in the following section.