Final answer:
To find the p-value for a standardized test statistic on a standard normal distribution, determine the relevant areas under the curve, based on the tail(s) of the distribution. For a right tail test for a difference in two proportions with z = 0.78, the p-value is 0.7823. For a left tail test for a difference in two means with z = -2.44, the p-value is 0.0075. For a two-tailed test for a proportion with z = 2.24, the p-value is 0.025.
Step-by-step explanation:
In order to find the p-value for a standardized test statistic, you need to determine the area under the standard normal distribution curve that is greater than or equal to the absolute value of the test statistic (since the p-value is based on the tail(s) of the distribution).
(a) For z = 0.78 in a right tail test for a difference in two proportions:
- Since it is a right tail test, you need to find the area to the right of 0.78 in the standard normal distribution.
- Using a z-table, the area to the right of 0.78 is approximately 0.2177.
- Therefore, the p-value is 1 - 0.2177 = 0.7823.
(b) For z = -2.44 in a left tail test for a difference in two means:
- Since it is a left tail test, you need to find the area to the left of -2.44 in the standard normal distribution.
- Using a z-table, the area to the left of -2.44 is approximately 0.0075.
- Therefore, the p-value is 0.0075.
(c) For z = 2.24 in a two-tailed test for a proportion:
- Since it is a two-tailed test, you need to find the area to the right of 2.24 and the area to the left of -2.24 in the standard normal distribution.
- Using a z-table, the area to the right of 2.24 is approximately 0.0125 and the area to the left of -2.24 is also approximately 0.0125.
- Therefore, the p-value is 2 * 0.0125 = 0.025.