Software analysis if the salaries of a random sample of 288

Software analysis if the salaries of a random sample of 288 Nevada teachers produced the confidence interval shown below. Which conclusion is correct? What\'s wrong with the others? with 90.00% confidence, t-interval for : 4354 < (TchPay) < 45398   a. If we took many random samples of Nevada teachers, about 9 our of 10 of the teachers would produce confidence interval that contained the mean salary of all Nevada teachers.   b. About 9 out of 10 of the teachers earn between $43,454 and $45,398. c. We are 90% confident that the average teacher salary in the United States is between $43,454 and $45,398.

Solution

ans : (C)

why A is wrong?

the confidence interval would depend on the value of sampling mean. Since we are using t-intervals, we must be using the sample error, which makes intervals even more variable than if we knew the true population standard deviation. Also, Its never the case with that our main interest in CI is to estimate the interval. We want to know how sure we are about the mean value lying in between the CI.

Why B is wrong?

The confidence interval is about the true population mean, about the probability that the true mean lies in the interval, not about the probability that a teacher earns an amount in this range.

C is true.