Questions: If you constructed one hundred 96% confidence intervals based on one hundred different random samples of size n, how many of the intervals would you expect to include the unknown parameter? Assume all model requirements are satisfied. Choose the correct answer below. A. 50 B. 100 C. 96 D. 4

If you constructed one hundred 96% confidence intervals based on one hundred different random samples of size n, how many of the intervals would you expect to include the unknown parameter? Assume all model requirements are satisfied.

Choose the correct answer below.
A. 50
B. 100
C. 96
D. 4

Transcript text: If you constructed one hundred $96 \%$ confidence intervals based on one hundred different random samples of size n, how many of the intervals would you expect to include the unknown parameter? Assume all model requirements are satisfied. Choose the correct answer below. A. 50 B. 100 C. 96 D. 4

Solution

Solution Steps

Step 1: Understanding the Confidence Interval

A confidence interval provides a range of values that is likely to contain the true parameter of interest. In this case, we are constructing $100$ different confidence intervals based on random samples, each with a confidence level of $96\%$.

Step 2: Calculating the Expected Number of Intervals

The expected number of intervals that will include the unknown parameter can be calculated using the formula:

\[ \text{Expected Intervals} = \text{Confidence Level} \times \text{Total Intervals} \]

Substituting the known values:

\[ \text{Expected Intervals} = 0.96 \times 100 = 96 \]

Step 3: Conclusion

Thus, we expect $96$ out of the $100$ constructed confidence intervals to include the unknown parameter.