Final answer:
The confidence interval estimate is calculated using the sample mean, the population standard deviation, the sample size, and the confidence level. The correct confidence interval for a 90% level of confidence, given the mean of 73.24, standard deviation of 25, and sample size of 50, is 73.24 ± 5.81.
Step-by-step explanation:
To calculate a confidence interval estimate for a population mean, we need the sample mean, the population standard deviation, the sample size, and the alpha level to determine the level of confidence. For this question, the sample mean is 73.24, the standard deviation is 25, the sample size (n) is 50, and the alpha level is 0.10, which corresponds to a 90% confidence level. The error bound for the mean (EBM) can be calculated using the z-score that corresponds with the alpha level and the standard deviation divided by the square root of the sample size. The z-score for a 90% confidence interval is approximately 1.645. The EBM is calculated as:
EBM = z * (sigma / √ n)
Which gives us:
EBM = 1.645 * (25 / √ 50)
Using this formula, calculate the EBM, and then add and subtract this value from the sample mean to get the confidence interval estimate.
The correct confidence interval estimate for this set of data is 73.24 ± 5.81.