Final answer:
The p-value for the given one-proportion z-test is 0.0764 or 7.64%.
Step-by-step explanation:
In a one-proportion z-test with p < 0.052, if z = -1.429961766, the p-value can be determined by finding the area to the right of the z-test in a standard normal distribution. The p-value is the probability of obtaining a test statistic more extreme than the observed test statistic, assuming the null hypothesis is true.
To calculate the p-value, we can use the standard normal distribution table or a calculator. In this case, the p-value is approximately 0.0764 or 7.64%, which is option a. 0.076364042.