Answer :
Final answer:
To test the seismologist's claim about earthquake depths, we first set up a two-tailed hypothesis test, calculate a test statistic using the sample mean, standard deviation, and size, and then determine the p-value to compare it with the significance level. After comparison, we conclude whether there is significant evidence against the null hypothesis that the mean depth is (C) 6.00 km. Hence, (C) is the correct option.
Explanation:
To address the original claim by a seismologist that these earthquakes come from a population with a mean depth of 6.00 km, we must first identify the null and alternative hypotheses.
The correct choice is C) H0: μ = 6.00 km and H1: μ ≠ 6.00 km, implying the seismologist believes the mean is not exactly 6.00 km but could be either less than or greater than 6.00 km - making it a two-tailed test.
Using the formula for a t-test, t = (x - μ) / (s / √n), where x is the sample mean, μ is the population mean under the null hypothesis, s is the sample standard deviation, and n is the sample size, we can calculate the test statistic in the event that the population standard deviation is unknown. We determine the value of the test statistic by substituting the supplied values, t = (6.72 - 6.00) / (4.71 / √600.
To find the p-value, we look this test statistic up in a t-distribution table or use statistical software. The p-value indicates the probability of observing a test statistic as extreme as, or more extreme than, the observed value under the null hypothesis.
Compare this p-value with the significance level, α = 0.01. If the p-value < α, we reject the null hypothesis, suggesting there is significant evidence to conclude the earthquake depths do not have a mean of 6.00 km.
Finally, based on whether the p-value is less than the significance level, we can either find significant or insufficient evidence to support the seismologist's claim that the mean depth of the population of earthquakes is not 6.00 km.
