a) The P-value for one-tailed test is 0.1335.
b) The P- value for two-tailed test is 0.2670.
To find the p-value for the test statistic z=1.11, we can use a standard normal table. The p-value is the probability of obtaining a test statistic as extreme or more extreme than z=1.11, assuming that the null hypothesis is true.
(a) Find the P-value for the test statistic z=1.11 for the following null and alternative hypotheses:
H0: The population mean is 19.
Ha: The population mean is less than 19.
This is a one-tailed test, because we are only interested in the probability of obtaining a test statistic that is less than z=1.11. To find the p-value, we look up the value of 1.11 in the standard normal table. This value is 0.1335. Since this is a one-tailed test, the p-value is 0.1335.
(b) Find the P-value for the test statistic z=1.11 for the following null and alternative hypotheses:
H0: The population mean is 19.
Ha: The population mean is not equal to 19.
This is a two-tailed test, because we are interested in the probability of obtaining a test statistic that is either less than z=1.11 or greater than z=-1.11. To find the p-value, we look up the value of 1.11 in the standard normal table and double it. This value is 0.2670. Therefore, the p-value is 0.2670.