Find the P-value for the indicated hypothesis test with the given standardized test statistics, z. Decide whether to reject H0 for the given level of significance a. two-tailed test with test statistic z= -1.57 and a=0.04
Find table in the back of your statistics text labeled something like "areas under normal distribution" to find the proportion/probability of Z = -1.57. Is that less than .04?
To find the p-value for a two-tailed hypothesis test, we need to calculate the probability that the absolute value of the standardized test statistic (|z|) is greater than or equal to the absolute value of the given test statistic (|z| = 1.57 in this case).
Since we have a two-tailed test, we need to find the probability for both the left tail and the right tail and then add them together to get the total p-value.
1. To find the probability for the left tail:
- Look up the z-value (-1.57) in the standard normal distribution table.
- The table will give you the area under the curve to the left of -1.57.
- Subtract this area from 0.5 (since it's a two-tailed test) to get the probability for the left tail.
2. To find the probability for the right tail:
- Look up the z-value (1.57) in the standard normal distribution table.
- The table will give you the area under the curve to the left of 1.57.
- Subtract this area from 0.5 (since it's a two-tailed test) to get the probability for the right tail.
3. Add the probability for the left tail and the probability for the right tail to get the total p-value.
Now let's calculate the p-value using the steps mentioned above.
1. To find the probability for the left tail:
- Looking up -1.57 in the z-table, we find an area of 0.0580.
- Subtracting this from 0.5, we get 0.5 - 0.0580 = 0.4420.
2. To find the probability for the right tail:
- Looking up 1.57 in the z-table, we find an area of 0.9419.
- Subtracting this from 0.5, we get 0.5 - 0.9419 = -0.4419.
3. Adding the probability for the left tail and the probability for the right tail:
- 0.4420 + 0.4419 = 0.8839.
The p-value for the given hypothesis test with a test statistic of z = -1.57 is approximately 0.8839.
Next, to decide whether to reject the null hypothesis (H0) or not, we compare the p-value with the level of significance (α = 0.04 in this case).
If the p-value is less than or equal to the level of significance (p-value <= α), we reject the null hypothesis. Otherwise, we fail to reject the null hypothesis.
Since the p-value (0.8839) is greater than the level of significance (0.04), we fail to reject H0 for the given level of significance.