P-Value worksheet

1. p-value: 0.02

1. Compare your statistic with the t distribution with 11 df, the curve it follows if nothing real is going on

   $t$$=2.8$

2. Find the area under the curve beyond your statistic, in one tail

   $\text{P(T >}2.8\text{)}$$=0.0086373845$

3. A two-tailed test counts results this extreme in either direction, so double it

   $p$$=2\times 0.0086373845$$=0.0172747691$

2. p-value: 0.11

1. Compare your statistic with the standard normal distribution, the curve it follows if nothing real is going on

   $z$$=1.6$

2. Find the area under the curve beyond your statistic, in one tail

   $\text{P(Z >}1.6\text{)}$$=0.0547992917$

3. A two-tailed test counts results this extreme in either direction, so double it

   $p$$=2\times 0.0547992917$$=0.1095985834$

3. p-value: 0.05

1. Compare your statistic with the t distribution with 11 df, the curve it follows if nothing real is going on

   $t$$=1.8$

2. The p-value is the area under the curve to the right of your statistic

   $p$$=\text{P(T >}1.8\text{)}$$=0.0496579466$

4. p-value: 0.13

1. Compare your statistic with the standard normal distribution, the curve it follows if nothing real is going on

   $z$$=1.5$

2. Find the area under the curve beyond your statistic, in one tail

   $\text{P(Z >}1.5\text{)}$$=0.0668072013$

3. A two-tailed test counts results this extreme in either direction, so double it

   $p$$=2\times 0.0668072013$$=0.1336144025$

5. p-value: 0.02

1. Compare your statistic with the t distribution with 12 df, the curve it follows if nothing real is going on

   $t$$=2.4$

2. The p-value is the area under the curve to the right of your statistic

   $p$$=\text{P(T >}2.4\text{)}$$=0.0167593251$

6. p-value: 0.02

1. Compare your statistic with the standard normal distribution, the curve it follows if nothing real is going on

   $z$$=2.4$

2. Find the area under the curve beyond your statistic, in one tail

   $\text{P(Z >}2.4\text{)}$$=0.0081975359$

3. A two-tailed test counts results this extreme in either direction, so double it

   $p$$=2\times 0.0081975359$$=0.0163950718$

7. p-value: 0.99

1. Compare your statistic with the chi-square distribution with 8 df, the curve it follows if nothing real is going on

   $\mathrm{\chi ²}$$=1.8$

2. The p-value is the area to the right of your statistic: 1 minus the area to its left

   $p$$=1-\text{P(χ² ≤}1.8\text{)}$$=0.9865412794$

8. p-value: 1

1. Compare your statistic with the chi-square distribution with 9 df, the curve it follows if nothing real is going on

   $\mathrm{\chi ²}$$=1.5$

2. The p-value is the area to the right of your statistic: 1 minus the area to its left

   $p$$=1-\text{P(χ² ≤}1.5\text{)}$$=0.9971467695$

9. p-value: 0.04

1. Compare your statistic with the standard normal distribution, the curve it follows if nothing real is going on

   $z$$=1.8$

2. The p-value is the area under the curve to the right of your statistic

   $p$$=\text{P(Z >}1.8\text{)}$$=0.0359303191$

10. p-value: 1

1. Compare your statistic with the chi-square distribution with 12 df, the curve it follows if nothing real is going on

   $\mathrm{\chi ²}$$=1.65$

2. The p-value is the area to the right of your statistic: 1 minus the area to its left

   $p$$=1-\text{P(χ² ≤}1.65\text{)}$$=0.9997829064$