Final answer:
To estimate the population mean with a 90% confidence level based on a sample mean of 150, a confidence interval is constructed by adding and subtracting the error bound for the mean (EBM) from the sample mean. This gives a range that would contain the true population mean in approximately 90% of repeated samples.
Step-by-step explanation:
To estimate the population mean with 90% confidence based on a sample mean of 150, you need to construct a confidence interval. The question provides an example where a sample mean is 15 and the error bound for the mean (EBM) is 3.2, which gives a 90% confidence interval estimate for the population mean. The interval is calculated by taking the sample mean and adding and subtracting the EBM, which in this example is from 15 - 3.2 to 15 + 3.2, yielding an interval from 11.8 to 18.2.
Using this method, we can create an estimated range for the population mean where, if we took repeated samples, approximately 90 percent of the confidence intervals from those samples would contain the true population mean. The confidence interval captures the essence that there is a central 90 percent probability that the sample mean will fall in this range, considering the normal distribution of sample means.
For the student's question where the sample mean is 150, and assuming a similar EBM is applicable (which would need to be calculated based on the population standard deviation and sample size), the confidence interval would be constructed in a similar manner. An example with a different mean and an EBM would adjust the interval accordingly, but the concept remains consistent.