Let's analyze this problem step-by-step.

The task involves evaluating confidence intervals from random samples to see how many contain the true population mean, $\mu = 140$. Here’s how to approach each part:

Part (a): 80% Confidence Intervals

1. Objective: Determine how many of the 80% confidence intervals contain the population mean $\mu = 140$.
2. Method: Look at each sample's 80% confidence interval in the table and/or graph and check if the interval includes 140.
3. Answering: Count the intervals that contain 140.

Part (b): 95% Confidence Intervals

1. Objective: Determine how many of the 95% confidence intervals contain $\mu = 140$.
2. Method: Look at each sample’s 95% confidence interval in the table and/or graph and check if the interval includes 140.
3. Answering: Count the intervals that contain 140.

Part (c): Choose All True Statements

For part (c), we will examine each statement to determine if it is true based on the information provided.

Instructions to Solve

Step-by-Step Analysis of Intervals

Go through the table or the graph:

1. For 80% confidence intervals, observe the lower and upper limits in the table for each sample (S1 to S20).
2. For 95% confidence intervals, repeat this process with the 95% limits.

Count the number of intervals that contain 140 in each case.

Would you like a detailed count of which specific intervals contain 140, or is this overview sufficient?

Practice Questions

1. How do you calculate a confidence interval for a given confidence level?
2. Why would a 95% confidence interval typically be wider than an 80% confidence interval?
3. How does the sample size affect the width of the confidence interval?
4. What is the interpretation of a confidence interval that does not contain the population mean?
5. How does changing the confidence level affect the probability of containing the population mean?

Tip

Remember: a confidence interval at a higher confidence level (e.g., 95%) is wider because it aims to capture the true mean with a higher probability than a narrower interval at a lower confidence level (e.g., 80%).