Chapter 1. The Reasoning of Statistical Estimation

Incorrect. Since \( \overline{x} \) does not equal µ, we have to know how accurately it estimates µ. In other words, we need a measure of the error, i.e., a measure of how far off \( \overline{x} \) could be from µ.

Correct. Since \( \overline{x} \) does not equal µ, we have to know how accurately it estimates µ. In other words, we need a measure of the error, i.e., a measure of how far off \( \overline{x} \) could be from µ.

Incorrect. Try again.

2

Incorrect. Before taking a sample, we do not know the value of \( \overline{x} \) so we can talk about the probability of \( \overline{x} \) being in some interval. But after we take a sample, we know the value of \( \overline{x} \) and we have "confidence" that this value is in an interval.

Correct. Before taking a sample, we do not know the value of \( \overline{x} \) so we can talk about the probability of \( \overline{x} \) being in some interval. But after we take a sample, we know the value of \( \overline{x} \) and we have "confidence" that this value is in an interval.

Incorrect. Try again.

2

Incorrect. The sampling distribution of \( \overline{x} \) provides us with probabilities on \( \overline{x} \) and a measure of the variability of \( \overline{x} \) with the standard deviation of the sampling distribution of \( \overline{x} \). We use both of these to find margin of error.

Correct. The sampling distribution of \( \overline{x} \) provides us with probabilities on \( \overline{x} \) and a measure of the variability of \( \overline{x} \) with the standard deviation of the sampling distribution of \( \overline{x} \). We use both of these to find margin of error.

Incorrect. Try again.

2

Incorrect. This is a correct statement.

Correct. This is a correct statement.

Incorrect. Try again.

2

Incorrect. We use \( \overline{x} \) to estimate µ. But since the value of \( \overline{x} \) does not equal the value of µ, we have error. Margin of error is a measure of this error.

Correct. We use \( \overline{x} \) to estimate µ. But since the value of \( \overline{x} \) does not equal the value of µ, we have error. Margin of error is a measure of this error.

Incorrect. Try again.

2

Incorrect. A confidence interval is an estimate of the value of a parameter. It is not intended to tell us a range of values for the data.

Correct. A confidence interval is an estimate of the value of a parameter. It is not intended to tell us a range of values for the data.

Incorrect. Try again.

2

Incorrect. This is exactly how we compute a confidence interval estimate for µ.

Correct. This is exactly how we compute a confidence interval estimate for µ.

Incorrect. Try again.

2

Incorrect. The value of \( \overline{x} \) is always between \( \overline{x} \) - ME and \( \overline{x} \) + ME. We can be 100% confident of that.

Correct. The value of is always between \( \overline{x} \) - ME and \( \overline{x} \) + ME. We can be 100% confident of that.

Incorrect. Try again.

2

Incorrect. If \( \overline{x} \) is between µ - ME and µ + ME, then µ will be between \( \overline{x} \) - ME and \( \overline{x} \) + ME.

Correct. If \( \overline{x} \) is between µ - ME and µ + ME, then µ will be between \( \overline{x} \) - ME and \( \overline{x} \) + ME.

Incorrect. Try again.

Incorrect. This is the idea behind a confidence interval. Just like the stake is invisible, the value of the parameter µ is unknown. We can compute margin of error similar to knowing the length of the rope. And we know the value of \( \overline{x} \) just like we know where the goat is. Using this information, we can get a good idea of where the stake is, i.e., we can get an estimate of what the value of µ is.

Correct. This is the idea behind a confidence interval. Just like the stake is invisible, the value of the parameter µ is unknown. We can compute margin of error similar to knowing the length of the rope. And we know the value of \( \overline{x} \) just like we know where the goat is. Using this information, we can get a good idea of where the stake is, i.e., we can get an estimate of what the value of µ is.

Incorrect. Try again.

2

Incorrect. This applet is intended to demonstrate this important fact.

Correct. This applet is intended to demonstrate this important fact.

Incorrect. Try again.

2

Incorrect. The interval (\( \overline{x} \) - ME, \( \overline{x} \) + ME) is a confidence interval estimate for µ, so it gives us a range of feasible values for µ.

Correct. The interval (\( \overline{x} \) - ME, \( \overline{x} \) + ME) is a confidence interval estimate for µ, so it gives us a range of feasible values for µ.

Incorrect. Try again.

2

Incorrect. Level of confidence is subjectively chosen by the researcher before data are collected.

Correct. Level of confidence is subjectively chosen by the researcher before data are collected.

Incorrect. Try again.

2