Confidence Interval Estimate of Mean with σ known?

2016-03-31 10:34 am

The population mean can be estimated from a sample group with Z-score if either the standard deviation of the corresponding population is known or the sample size is large.

1. An analyst collected a simple random sample of n = 36 customers from a population of students of age 12, which gives the sample mean height of students as 125cm. It is known that the population standard deviation of height of students is 24cm.

a) Construct a 99 percent confidence interval for the population mean μ.

b) To interpret the interval, the analyst states that he has 99 percent confidence that the population mean height of students is between 114.7cm to 135.3cm. Explain the meaning of this statement.

I need the calculation steps, thank you very much!!!

回答 (1)

[匿名]

2016-04-01 5:31 am

✔ 最佳答案

a) 125+-z*24/sqrt(36)
b) First, it is important to understand that this statement DOES NOT mean there is a 99% chance the population mean is between the boundaries. What it does mean is that if the experiment were repeated in the same manner, then AT LEAST 99% of the time the chosen confidence intervals will contain the parameter. It is impossible to know if the parameter is inside the interval. It is also impossible to make a probability statement about the chance the parameter is inside the interval. To accomplish that, you would instead need to use a Bayesian statistical method.

The confidence is in the procedure itself and not in the particular solution for this one sample.

👍 0 👎 1