Final answer:
The hypothesis test is a right-tailed test. The P-value should be calculated by finding the area to the right tail of the test statistic. The decision to reject or fail to reject the null hypothesis depends on the comparison between the P-value and the significance level.
Step-by-step explanation:
The hypothesis test described here is a right-tailed test because the claim being tested is that the proportion, p, is greater than 0.8. The null hypothesis, H0, states that p is less than or equal to 0.8, while the alternative hypothesis, Ha, states that p is greater than 0.8.
To find the P-value, we need to calculate the probability of observing a test statistic as extreme as 0.68 or more extreme, assuming the null hypothesis is true. Since the test statistic, z, is positive, we calculate the area to the right tail of 0.68 in a standard normal distribution to find the P-value.
To determine whether to reject or fail to reject the null hypothesis, we compare the P-value to the desired significance level, usually denoted as α. If the P-value is less than α, we reject the null hypothesis. If the P-value is greater than or equal to α, we fail to reject the null hypothesis.