If we construct 1000 confidence intervals for the population mean with 97% confidence level using the same method and not changing sample size, we expect

Question

of them to contain the true population mean.

Answer 1

When constructing confidence intervals, the confidence level represents the proportion of intervals that we expect to contain the true population parameter. In this case, you are using a 97% confidence level, which means that we expect 97% of the confidence intervals to contain the true population mean.

If you construct 1000 confidence intervals, you would expect:

\[ 0.97 \times 1000 = 970 \]

So, we expect 970 of the 1000 confidence intervals to contain the true population mean.