Find the p-value for each test statistic. a. Right-tailed test, z=+1.34 b. Left-tailed test, z=−2.07 c. Two-tailed test, z=−1.69

The p-value is the actual level of the test statistic. It represents the probability of getting a result as extreme as the test statistic itself. To determine this probability, use a z-table with the z-values given.

To find the p-value for each test statistic, you need to use a standard normal distribution table or a statistical calculator. The p-value represents the probability of observing a test statistic as extreme or more extreme than the given value, assuming the null hypothesis is true.

a. Right-tailed test, z=+1.34:
For a right-tailed test, the p-value is the probability of observing a test statistic as large or larger than the given value. In this case, you have z=+1.34. To find the p-value, you need to find the area under the standard normal curve to the right of +1.34.

Using a standard normal distribution table, you can find the area to the right of +1.34, which is equivalent to 1 - the cumulative area to the left of +1.34. The table or calculator will give you a value of 0.0901. Therefore, the p-value for this test statistic is approximately 0.0901.

b. Left-tailed test, z=−2.07:
For a left-tailed test, the p-value is the probability of observing a test statistic as small or smaller than the given value. In this case, you have z=−2.07. To find the p-value, you need to find the area under the standard normal curve to the left of −2.07.

Using a standard normal distribution table, you can find the area to the left of −2.07, which is equivalent to the cumulative area to the left of −2.07. The table or calculator will give you a value of 0.0188. Therefore, the p-value for this test statistic is approximately 0.0188.

c. Two-tailed test, z=−1.69:
For a two-tailed test, the p-value is the probability of observing a test statistic as extreme or more extreme than the absolute value of the given value, in either the positive or negative tail of the distribution. In this case, you have z=−1.69. To find the p-value, you need to find the area under the standard normal curve in both tails, around the absolute value of −1.69.

Using a standard normal distribution table, you can find the area to the left of −1.69, which is equivalent to the cumulative area to the left of −1.69. The table or calculator will give you a value of 0.0459. Since this is a two-tailed test, you need to double this value to account for both tails. Therefore, the p-value for this test statistic is approximately 2 * 0.0459 = 0.0918.