The manager of an aquatic center is interested in the average number of fish people keep in their saltwater tanks. She randomly selects 38 people who own saltwater fish tanks and asks how many fish they have. The mean number of fish is 48.2 with a standard deviation of 22.1 fish. Which of the following is the 99% confidence interval for the true mean number of fish in saltwater tanks?Find the t-table here.

Because the population standard deviation is not given, use a t-interval with 38 − 1 = 37 degrees of freedom. For 99% confidence, the critical value is about 2.715, and the standard error is 22.1/√38 ≈ 3.58. The margin of error is 2.715 × 3.58 ≈ 9.73, so the interval is 48.2 ± 9.73, or approximately (38.47, 57.94). Thus, the 99% confidence interval is choice A.

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