Answer:
95%
Explanation:
Based on the given information, the confidence interval (4, 10) has been constructed using a sample size of 52 and a known population standard deviation of 17.638. To determine the confidence level used for this interval, we can compare the interval to the standard normal distribution (Z-distribution) for the corresponding critical values.
The formula for the confidence interval for a population mean with known standard deviation is given by:
Confidence interval = Sample mean ± (Z critical value * (Population standard deviation / sqrt(sample size)))
In this case, the given confidence interval is (4, 10), which represents the range of possible values for the population mean. The sample mean is not provided in the given information, so we cannot determine the exact confidence level used.
However, based on the provided answer choices, the closest match to the given confidence interval would be a 95% confidence level. This is because the confidence interval (4, 10) is quite wide, which corresponds to a higher level of confidence. A 95% confidence level is commonly used in many statistical analyses as it provides a high level of confidence in the estimated interval. Therefore, the most likely answer would be 95%.