Final answer:
When using a z-test to test the null hypothesis, H_{0}: p=0.4, against the alternative hypothesis, H_{a}: p>0.4, with a given z-score of 1.42, the p-value is approximately 0.0788. Since the p-value is greater than the chosen significance level of 0.05, we fail to reject the null hypothesis.
Step-by-step explanation:
In this situation, we are using a z-test to test the null hypothesis, H0: p = 0.4, against the alternative hypothesis, Ha: p > 0.4. To determine the p-value, we need to compare the test statistic (z-score) calculated from the data with the critical value for our chosen significance level, α = 0.05. If the test statistic is greater than the critical value, we reject the null hypothesis. In this case, the given z-score is 1.42. To find the p-value, we need to find the area to the right of 1.42 under the standard normal distribution curve. Using a z-table or calculator, we find that the p-value is approximately 0.0788. Since the p-value is greater than α (0.0788 > 0.05), we fail to reject the null hypothesis. This means that there is not enough evidence to support the claim that p is greater than 0.4.