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StatTutor Lesson - Margin of Error and Confidence Level

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      Questions 1-2

      123

      Question 1.

      In general, what is µ?

      A.
      B.
      C.

      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.
      Incorrect. Try again.
      2

      Question 3

      201

      Question 3.

      True or false: Margin of error is a measure of how far off ¯x could be from µ.

      A.
      B.

      Incorrect. Margin of error is a measure of how accurately ¯x estimates µ. If confidence is 95%, it tells us the most that ¯x could differ from µ for the middle 95% of all possible ¯x-values.
      Correct. Margin of error is a measure of how accurately ¯x estimates µ. If confidence is 95%, it tells us the most that ¯x could differ from µ for the middle 95% of all possible ¯x-values.
      Incorrect. Try again.
      2

      Question 4

      328

      Question 4.

      A 90% confidence interval for µ is (11.5, 12.3). What does 90% level of confidence tell us?

      A.
      B.
      C.

      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.
      Incorrect. Try again.
      2

      Questions 5-6

      454

      Question 5.

      A 90% confidence interval for µ is (11.5, 12.3). What is the probability that the value of µ is in this interval?

      A.
      B.

      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.
      Incorrect. Try again.
      2

      Question 7

      474

      Question 7.

      When does a researcher chose level of confidence?

      A.
      B.

      Incorrect. Ethically, level of confidence should be chosen before data are collected.
      Correct. Ethically, level of confidence should be chosen before data are collected.
      Incorrect. Try again.
      2

      Question 8

      604

      Question 8.

      If you chose 99% confidence rather than 90% confidence, will your confidence interval be wider or narrower?

      A.
      B.

      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.
      Incorrect. Try again.
      2

      Question 9

      740

      Question 9.

      A 90% confidence interval for µ is (11.5, 12.3). What is a correct interpretation of this interval?

      A.
      B.
      C.

      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.
      Incorrect. Try again.
      2