# Variance and Sketching P-Values

1. In this test, the variance is known. Find the p-value of the test to 4 decimals, if the obtained value of the test statistic is 2.34. Make a sketch and represent the p-value.

H_o : Mu = Mu_o

H_a : Mu ,not = to, Mu_o

2. In this test, the variance is known. Find the p-value of the test to 4 decimals, if the obtained value of the test statistic is 1.45. Make a sketch and represent the p-value.

H_o : Mu ,> equal to, Mu_o

H_a : Mu < Mu_o

3. In this test, the variance is unknown and the sample size is 15. Bracket the p-value of the test, if the obtained value of the test statistic is 2.05.

H_o : Mu = Mu_o

H_a : Mu ,not = to, Mu_o

4. In this test, the population is normal, and the sample size is 20. Bracket the p-value of the test, if the obtained value of the test statistic is 31.786.

H_o : sigma square ,< equal to, 36

H_a : sigma square > 36

#### Solution Preview

...istic 2.34 is 0.0192837

2. In this test, the variance is known. Find the p-value of the test to 4 decimals, if the obtained value of the test statistic is 1.45. Make a sketch and represent the p-value as an area under the PDF

H_o : Mu ,> equal to, Mu_o

H_a : Mu < Mu_o

Solution:

The p ...