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Answer :
Final answer:
To calculate the 95% confidence interval for the population mean, the formula includes the sample mean, standard deviation, sample size, and the t-score for a 95% confidence level. The correct confidence interval based on the data provided is approximately (472.588, 512.012), which is closest to option a. (475.8, 508.8), although no options match perfectly.
Explanation:
To construct a 95% confidence interval for the population mean, we need to use the sample mean, standard deviation, and the size of the sample along with a t-score because our sample size is less than 30. For a confidence level of 95%, and with degrees of freedom as 17 (n-1 for 18 subjects), we look up the t-score in a t-distribution table or use a calculator that gives us the t-score for 95% confidence interval which is close to 2.110.
The formula for the confidence interval is mean ± (t-score * (standard deviation / √n)). Substituting the given values we get 492.3 ± (2.110 * (37.6 / √18)). Calculating the margin of error, we have 2.110 * (37.6 / 4.243) which equals approximately 19.712. Therefore, the confidence interval is 492.3 ± 19.712, giving us the interval (472.588, 512.012).
Comparing our calculation with the provided options, none of the options match our calculated confidence interval perfectly. However, the closest approximate answer, considering rounding error, is option a. (475.8, 508.8).
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