Final answer:
The correct answer is option b. In a right-tailed test, the p-value corresponding to a z-test statistic of 1.47 is approximately 0.0708, indicating a 7.08% chance of obtaining such an extreme test statistic if the null hypothesis were true.
Step-by-step explanation:
In a right-tailed test, if a statistician gets a z-test statistic of 1.47, we're interested in finding the p-value, which is the probability of observing a value as extreme or more extreme than the test statistic, given that the null hypothesis is true. To find this p-value in a standard normal distribution (a Z-distribution), we need to find the area to the right of the z-value 1.47.
We can do that using a Z-table, statistical software, or a calculator with statistical functions. However, based on the data provided which doesn't exactly match the query, we can estimate that the p-value is close to the cumulative probability up to 1.47 in the Z-distribution. This can typically be found in the tail end of the Z-table, which gives us the p-value associated with our statistic. Since this is not provided, we refer to standard normal distribution tables or software to find that the p-value associated with a Z-statistic of 1.47 is approximately 0.0708. This means that if the null hypothesis is true, there is a 7.08% chance of obtaining a test statistic as extreme as 1.47 or more in the direction of the alternative hypothesis.