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Question 1:
Did your 95% confidence interval contain (or “cover”) the population mean μ (the green
line)?
The 95% confidence interval did cover the population mean.
Question 2:
Was your second sample mean x-bar (the new red dot) the same value as your 1st sample
mean? (i.e., is it in the same relative location along the axis?) Why is this result to be
expected?
The second sample mean was not the same as the first sample mean. This result was to be
expected due to the samples being continuously distributed over the axis.
Question 3:
A new 95% confidence interval has also been constructed (the new line segment, centered
at the location of your second x-bar). Does the new interval cover the population mean μ?
The new 95% confidence interval that has been constructed also covers the population mean
Question 4:
What percentage of the many 95% confidence intervals should cover the population mean
μ?
96.51% of the 95% confidence interval should cover the population mean
Question 5:
Now let’s summarize some key ideas. Based on what you’ve seen on the simulation (with
the level set at 95%), decide which of the following statements are true and which are false
1. Each interval is centered at the population mean (μ). False
2. Each interval is centered at the sample mean (x-bar). True
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3. The population mean (μ) changes when different samples are selected. False
4. The sample mean (x-bar) changes when different samples are selected. True
5. In the long run, 95% of the intervals will contain (or “cover”) the sample mean (x-bar). False
6. In the long run, 95% of the intervals will contain (or “cover”) the population mean (μ). True

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Question 1: Did your 95% confidence interval contain (or “cover”) the population mean μ (the green line)? The 95% confidence interval did cover the population mean. Question 2: Was your second sample mean x-bar (the new red dot) the same value as your 1st sample mean? (i.e., is it in the same relative location along the axis?) Why is this result to be expected? The second sample mean was not the same as the first sample mean. This result was to be expected due to the samples being continuously distributed over the axis. Question 3: A new 95% confidence interval has also been constructed (the new line segment, centered at the location of your second x-bar). Does the new interval cover the population mean μ? The new 95% confidence interval that has been constructed also covers the population mean Question 4: What percentage of the many 95% confidence intervals should cover the population mean μ? 96.51% of the 95% confidence interval should cover the population mean Question 5: Now let’s summarize some key ideas. Based on what you’ve seen on the simulation (with the level set at 95%), decide which of the following statements are true and which are false 1. Each interval is centered at the population mean (μ). False 2. Each interval is centered at the sample mean (x-bar). True 3. The population mean (μ) changes when different samples are selected. False 4. The sample mean (x-bar) changes when different samples are selected. True 5. In the long run, 95% of the intervals will contain (or “cover”) the sample mean (x-bar). False 6. In the long run, 95% of the intervals will contain (or “cover”) the population mean (μ). True Name: Description: ...
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