Chapter 1. Margin of Error and Confidence Level

Incorrect. µ is the population mean, so it is the mean response of all individuals in the population.

Correct. µ is the population mean, so it is the mean response of all individuals in the population.

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Incorrect. A 95% confidence interval for µ is the interval (\( \overline{x} \) - ME, \( \overline{x} \) + ME) or (39.6 - 1.2, 39.6 + 1.2) or (38.4, 40.8).

Correct. A 95% confidence interval for µ is the interval (\( \overline{x} \) - ME, \( \overline{x} \) + ME) or (39.6 - 1.2, 39.6 + 1.2) or (38.4, 40.8).

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Incorrect. Margin of error is a measure of how accurately \( \overline{x} \) estimates µ. If confidence is 95%, it tells us the most that \( \overline{x} \) could differ from µ for the middle 95% of all possible \( \overline{x} \)-values.

Correct. Margin of error is a measure of how accurately \( \overline{x} \) estimates µ. If confidence is 95%, it tells us the most that \( \overline{x} \) could differ from µ for the middle 95% of all possible \( \overline{x} \)-values.

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Incorrect. Confidence level tells us the percentage of all possible confidence intervals for µ that will contain the value of µ. So 90% confidence tells us that 90% of all possible 90% confidence intervals will contain the value of µ.

Correct. Confidence level tells us the percentage of all possible confidence intervals for µ that will contain the value of µ. So 90% confidence tells us that 90% of all possible 90% confidence intervals will contain the value of µ.

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Incorrect. Even if a basketball player is a 90% free throw shooter, when she takes a freethrow shot, she either makes or misses the shot. Similarly, a confidence interval is just like taking a freethrow shot. A specific interval either captures the value of a parameter or misses it. Thus, the probability is either zero or one that the value of µ is in this confidence interval. A 90% free throw shooter makes 90% of all of her free throw shots and 90% confidence means that 90% of all possible intervals contain the value of the parameter.

Correct. Even if a basketball player is a 90% free throw shooter, when she takes a freethrow shot, she either makes or misses the shot. Similarly, a confidence interval is just like taking a freethrow shot. A specific interval either captures the value of a parameter or misses it. Thus, the probability is either zero or one that the value of µ is in this confidence interval. A 90% free throw shooter makes 90% of all of her free throw shots and 90% confidence means that 90% of all possible intervals contain the value of the parameter.

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Incorrect. A free throw shooter makes 90% of her free throw shots. However, she cannot make 90% of one free throw shot. Similarly, one 90% confidence interval either contains the value of µ or it does not. But 90% of all 90% confidence intervals for µ actually contain the value of µ.

Correct. A free throw shooter makes 90% of her free throw shots. However, she cannot make 90% of one free throw shot. Similarly, one 90% confidence interval either contains the value of µ or it does not. But 90% of all 90% confidence intervals for µ actually contain the value of µ.

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Incorrect. Ethically, level of confidence should be chosen before data are collected.

Correct. Ethically, level of confidence should be chosen before data are collected.

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Incorrect. Higher confidence gives a larger margin of error which results in a wider confidence interval.

Correct. Higher confidence gives a larger margin of error which results in a wider confidence interval.

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2

Incorrect. When we interpret a confidence interval, we state our confidence in the interval containing the value of µ. We cannot use the term "probability" after the sample has been taken. Further, one interval either contains the value of µ or it does not. We cannot say "90% of the time" with reference to one specific confidence interval.

Correct. When we interpret a confidence interval, we state our confidence in the interval containing the value of µ. We cannot use the term "probability" after the sample has been taken. Further, one interval either contains the value of µ or it does not. We cannot say "90% of the time" with reference to one specific confidence interval.

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