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StatTutor Lesson - Inference about Prediction

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      Question 1

      65

      Question 1.

      Which is bigger, standard deviation or standard error of ¯x?

      A.
      B.

      Correct. Standard deviation is bigger than standard error of ¯x.
      Incorrect.Standard deviation is bigger than standard error of ¯x.
      2
      Try again.

      Question 2

      117

      Question 2.

      True or false: Predictions made using a least-squares regression line have errors.

      A.
      B.

      Correct. This is a correct statement.
      Incorrect. This is a correct statement.
      2
      Try again.

      Question 3

      203

      Question 3.

      True or false: The value for the predicted tree volume, , when tree diameter X = 11 is computed as ˆy=36.946(11)+5.066.

      A.
      B.

      Correct. The value for is computed as ˆy=36.946+5.066(11).
      Incorrect. The value for is computed as ˆy=36.946+5.066(11).
      2
      Try again.

      Question 4

      297

      Question 4.

      Which of the following does ˆy estimate?

      A.
      B.
      C.

      Correct. ˆy estimates both the mean board feet of all trees with sixteen inch diameters and the volume of wood in hundred board feet for one particular tree having a sixteen inch diameter.
      Incorrect. ˆy estimates both the mean board feet of all trees with sixteen inch diameters and the volume of wood in hundred board feet for one particular tree having a sixteen inch diameter.
      2
      Try again.

      Question 5

      340

      Question 5.

      True or false: The error on the prediction of the mean board feet of all trees is the same as the error on the prediction of the volume of wood in board feet of a particular tree.

      A.
      B.

      Correct. The two interpretations for the prediction have different error estimates.
      Incorrect. The two interpretations for the prediction have different error estimates.
      2
      Try again.

      Questions 6-8

      408

      Question 6.

      Which interval estimates the mean volume of wood for all trees with sixteen inch diameters?

      A.
      B.

      Correct. A confidence interval for μY estimates the mean volume of wood for all trees with sixteen inch diameters.
      Incorrect. A confidence interval for μY estimates the mean volume of wood for all trees with sixteen inch diameters.
      2
      Try again.

      Question 9

      414

      Question 9.

      Fill in the blank: A prediction interval for an individual is ____________________ a confidence interval for a mean.

      A.
      B.
      C.

      Correct. A prediction interval for an individual is wider than a confidence interval for the mean, μY.
      Incorrect. A prediction interval for an individual is wider than a confidence interval for the mean, μY.
      2
      Try again.

      Questions 10-11

      480

      Question 10.

      What is ˆy called in the Minitab output?

      A.
      B.
      C.
      D.
      E.

      Correct. ˆy is called “Fit” in the Minitab output.
      Incorrect. ˆy is called “Fit” in the Minitab output.
      2

      Questions 12

      560

      Question 12.

      True or false: All confidence intervals have the form: “estimate” ± “table value” times “S.E. of estimate”.

      A.
      B.

      Correct. This is a true statement.
      Incorrect. This is a true statement.
      2

      Questions 13

      581

      Question 13.

      What table is used to find the “table value” for a confidence interval for the mean, μY.

      A.
      B.
      C.

      Correct. The t table is used to find the “table value” for a confidence interval for the mean, μY.
      Incorrect. The t table is used to find the “table value” for a confidence interval for the mean, μY.
      2

      Questions 14

      594

      Question 14.

      What is the name of s1n, the part of the formula highlighted in pink?

      A.
      B.

      2
      Correct. s1n is the standard error of ¯x.
      Incorrect. s1n is the standard error of ¯x.

      Questions 15-16

      764

      Question 15.

      What is estimated with the interval (42.02, 46.20)?

      A.
      B.

      Correct. This is a confidence interval for μY, the mean board feet for all sixteen inch diameter trees.
      Incorrect. This is a confidence interval for μY, the mean board feet for all sixteen inch diameter trees.
      2

      Question 17

      801

      Question 17.

      For this example, what is the margin of error of the prediction?

      A.
      B.
      C.
      D.

      Correct. The margin of error is 1.931.
      Incorrect. The margin of error is 1.931.
      2

      Question 18

      852

      Question 18.

      True or false: A prediction made using an x value close to ¯x is more accurate than a prediction made using an x value that is far from ¯x.

      A.
      B.

      Correct. Part of “SEˆμ” is (x¯x)2 where x is the value of x used in prediction. Since (x¯x)2 is smaller when x is closer to ¯x, predictions are more accurate if x is closer to ¯x.
      Incorrect. Part of “SEˆμ” is (x¯x)2 where x is the value of x used in prediction. Since (x¯x)2 is smaller whenx is closer to ¯x, predictions are more accurate if x is closer to ¯x.
      2

      Question 19

      918

      Question 19.

      True or false: ˆy estimates the volume of wood for one particular tree having sixteen inch diameter whereas ¯y estimates the mean board feet for all trees with sixteen inch diameter.

      A.
      B.

      Correct. ˆy estimates both the volume of wood for one particular tree having sixteen inch diameter and the mean board feet for all trees with sixteen inch diameters. ˆy can have either these two interpretations.
      Incorrect. This is a correct statement.
      2

      Question 20

      969

      Question 20.

      True or false: The estimate used in a prediction interval for an individual is the same as the estimate used in the confidence interval for the mean.

      A.
      B.

      Correct. The estimate for a prediction interval is ˆy. The estimate used in a confidence interval for the mean is also ˆy. Both intervals use the same estimate.
      Incorrect. The estimate for a prediction interval is ˆy. The estimate used in a confidence interval for the mean is also ˆy. Both intervals use the same estimate.
      2

      Question 21

      1035

      Question 21.

      What is the name of "s1", that portion of the formula highlighted in pink?

      A.
      B.

      Correct. "s1" is standard deviation.
      Incorrect. "s1" is standard deviation.
      2

      Question 22

      1137

      Question 22.

      What does the interval (35.17, 53.05) estimate?

      A.
      B.

      Correct. The interval estimates y, the volume of wood in 100 board feet of one tree having a sixteen inch diameter.
      Incorrect. The interval estimates y, the volume of wood in 100 board feet of one tree having a sixteen inch diameter.
      2

      Question 23

      1290

      Question 23.

      Which interval is wider?

      A.
      B.

      Correct. Prediction intervals as given by the blue bands in the graphic are wider than the confidence intervals given by the red bands.
      Incorrect. Prediction intervals as given by the blue bands in the graphic are wider than the confidence intervals given by the red bands.
      2

      Question 24

      1306

      Question 24.

      Fill in the blank: A confidence interval for the mean based on standard error of ¯x is _____________ a prediction interval for an individual based on standard deviation.

      A.
      B.
      C.

      Correct. A confidence interval for the mean is narrower than a prediction interval for an individual because it is based on standard error of ¯x which is smaller than standard deviation. A prediction interval is based on standard deviation.
      Incorrect. A confidence interval for the mean is narrower than a prediction interval for an individual because it is based on standard error of ¯x which is smaller than standard deviation. A prediction interval is based on standard deviation.
      2