100 random samples are taken to estimates the mean μ. A 95% confidence interval on the mean is 0.49 ≤ μ ≤ 0.82. Consider the following statement:There is a 95% chance that μ is between 0.49 and 0.82.Is the statement correct? Explain your answer.I suppose the statement is wrong and the right one must be: There is a 95% chance that μ is actually in some interval that are found.For example, by researching, I found 100 different intervals and 95 of them contains μ in average.

Question

100  random samples are taken to estimates the mean   μ. A 95% confidence interval on the mean is   0.49  ≤  μ  ≤  0.82. Consider the following statement:There is a 95% chance that   μ is between 0.49 and 0.82.Is the statement correct? Explain your answer.I suppose the statement is wrong and the right one must be: There is a 95% chance that   μ is actually in some interval that are found.For example, by researching, I found 100 different intervals and 95 of them contains   μ in average.

Sharon Dawson · Accepted Answer

Step 1  μ for the population either is or is not in the interval - it&#039;s a binary thing, there is no &quot;chance&quot; of it being anywhere. On the other hand, what this 95% confidence basically means is that, if you were to generate many, many samples each with their own mean, and used those sample means             x      ¯       to generate likewise 95% confidence intervals, about 95% of those generated intervals would in fact contain the population mean   μ.For any particular interval,   μ is either in it or it&#039;s not. There is no chance of it, it&#039;s only a single interval after all. But if you were to generate many confidence intervals, on average, you would expect about 95% of them to contain   μ.Step 2Or phrased differently yet again, from a huge bunch of confidence intervals generated this way, you could uniformly randomly pick one interval containing   μ with 95% probability. The chosen interval either does or doesn&#039;t. But you&#039;d have an about 95% chance at picking such an interval.

100 random samples are taken to estimates the mean mu. A 95% confidence interval on the mean is 0.49 <= mu <= 0.82. Consider the following statement: There is a 95% chance that mu is between 0.49 and 0.82. Is the statement correct? Explain your answer.

Answered question

Answer & Explanation

New Questions in College Statistics