Final answer:
To determine if a study's sample mean is significantly different from the population mean, a hypothesis test like the z-test is used. The null hypothesis states there is no difference, while the alternative hypothesis states there is a significant difference.
Step-by-step explanation:
To determine if you should accept or reject the study as having a mean significantly different from the population mean, you can conduct a hypothesis test. Since the population standard deviation is not given, you would typically use a t-test; however, the question seems to imply that we should assume the population standard deviation based on the sample. Let us go ahead with a z-test due to this confusion. Using the given sample mean of 9.5, sample standard deviation of 11, and sample size of 16, you can calculate the z-score and compare it to the critical z-value at a 90% confidence level.
The null hypothesis (H0) would be that the mean lifespan of pet goldfish is 12 years (no difference), and the alternative hypothesis (H1) would be that the mean is not 12 years (there is a significant difference). If the calculated z-score is greater than the critical z-value, we reject the null hypothesis, indicating the sample mean is significantly different from the population mean.