Chapter 1. Inference about Prediction

Correct. Standard deviation is bigger than standard error of \( \overline{x} \).

Incorrect.Standard deviation is bigger than standard error of \( \overline{x} \).

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Try again.

Correct. This is a correct statement.

Incorrect. This is a correct statement.

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Correct. The value for is computed as \(\widehat{y} = -36.946 + 5.066(11)\).

Incorrect. The value for is computed as \(\widehat{y} = -36.946 + 5.066(11)\).

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Correct. \(\widehat{y} \) 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. \(\widehat{y} \) 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.

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Correct. The two interpretations for the prediction have different error estimates.

Incorrect. The two interpretations for the prediction have different error estimates.

2

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Correct. A confidence interval for μ_Y estimates the mean volume of wood for all trees with sixteen inch diameters.

Incorrect. A confidence interval for μ_Y estimates the mean volume of wood for all trees with sixteen inch diameters.

2

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Correct. A prediction interval for y estimates the volume of wood for a particular tree with sixteen inch diameter.

Incorrect. A prediction interval for y estimates the volume of wood for a particular tree with sixteen inch diameter.

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Try again.

Correct. The two interpretations for the prediction have different error estimates. Since the interval estimating the mean (4,202, 4,620) is narrower than the interval estimating the volume of a particualr tree (3,517, 5,306), the error for the mean volume in board feet is less than the error for the board feet of a particular tree.

Incorrect. The two interpretations for the prediction have different error estimates. Since the interval estimating the mean (4,202, 4,620) is narrower than the interval estimating the volume of a particualr tree (3,517, 5,306), the error for the mean volume in board feet is less than the error for the board feet of a particular tree.

2

Try again.

Correct. A prediction interval for an individual is wider than a confidence interval for the mean, μ_Y.

Incorrect. A prediction interval for an individual is wider than a confidence interval for the mean, μ_Y.

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Correct. \(\widehat{y} \) is called “Fit” in the Minitab output.

Incorrect. \(\widehat{y} \) is called “Fit” in the Minitab output.

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Correct. \(\widehat{y} \) is called “Predict.y” in the CrunchIt! 2.0 output.

Incorrect. \(\widehat{y} \) is called “Predict.y” in the CrunchIt! 2.0 output.

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Correct. This is a true statement.

Incorrect. This is a true statement.

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

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

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2

Correct. \(s \sqrt{ \frac{1}{n} } \) is the standard error of \( \overline{x} \).

Incorrect. \(s \sqrt{ \frac{1}{n} } \) is the standard error of \( \overline{x} \).

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

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

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Correct. The margin of error is 2.092.

Incorrect. The margin of error is 2.092.

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Correct. The margin of error is 1.931.

Incorrect. The margin of error is 1.931.

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Correct. Part of “\(SE_{ \widehat{ \mu } } \)” is \(( x^{*} - \overline{x} )^{2} \) where \( x^{*} \) is the value of x used in prediction. Since \(( x^{*} - \overline{x} )^{2} \) is smaller when \( x^{*} \) is closer to \( \overline{x} \), predictions are more accurate if \( x^{*} \) is closer to \( \overline{x} \).

Incorrect. Part of “\(SE_{ \widehat{ \mu } } \)” is \(( x^{*} - \overline{x} )^{2} \) where \( x^{*} \) is the value of x used in prediction. Since \(( x^{*} - \overline{x} )^{2} \) is smaller when\( x^{*} \) is closer to \( \overline{x} \), predictions are more accurate if \( x^{*} \) is closer to \( \overline{x} \).

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Correct. \(\widehat{y} \) 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. \(\widehat{y} \) can have either these two interpretations.

Incorrect. This is a correct statement.

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Correct. The estimate for a prediction interval is \(\widehat{y} \). The estimate used in a confidence interval for the mean is also \(\widehat{y} \). Both intervals use the same estimate.

Incorrect. The estimate for a prediction interval is \(\widehat{y} \). The estimate used in a confidence interval for the mean is also \(\widehat{y} \). Both intervals use the same estimate.

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Correct. "\(s \sqrt{1} \)" is standard deviation.

Incorrect. "\(s \sqrt{1} \)" is standard deviation.

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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.

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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.

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Correct. A confidence interval for the mean is narrower than a prediction interval for an individual because it is based on standard error of \( \overline{x} \) 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 \( \overline{x} \) which is smaller than standard deviation. A prediction interval is based on standard deviation.

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Correct. The alternative hypothesis can be stated one of two ways: “Size can be used to predict price” or “There is a linear relationship between size and price.”

Incorrect. The alternative hypothesis can be stated one of two ways: “Size can be used to predict price” or “There is a linear relationship between size and price.”

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Correct. Price of a diamond only increases with size; price of a diamond never decreases as size increases.

Incorrect. Price of a diamond only increases with size; price of a diamond never decreases as size increases.

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Correct. P-value for testing slope is found on the bottom row of the output in the “P-Value” column. For thse data, the P-value is <0.0001.

Incorrect. P-value for testing slope is found on the bottom row of the output in the “P-Value” column. For thse data, the P-value is <0.0001.

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Correct. No megaphone pattern is visible so constant standard deviation condition is ok.

Incorrect. No megaphone pattern is visible so constant standard deviation condition is ok.

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Correct. No smile or frown pattern in the residual plot so linearity condition is ok.

Incorrect. No smile or frown pattern in the residual plot so linearity condition is ok.

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Correct. With no outlier in the histogram of residuals, the Normality condition is ok.

Incorrect. With no outlier in the histogram of residuals, the Normality condition is ok.

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Correct. Since P-value < 0.0001 is less than α = 0.05, we can reject the null hypothesis.

Incorrect. Since P-value < 0.0001 is less than α = 0.05, we can reject the null hypothesis.

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Correct. One way to state the alternative hypothesis is to say that “X can be used to predict Y.” In this case we can say that size can be used to predict price if we reject the null hypothesis.

Incorrect. One way to state the alternative hypothesis is to say that “X can be used to predict Y.” In this case we can say that size can be used to predict price if we reject the null hypothesis.

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Correct. Since there is a significant linear relationship, we can use size to predict price, but only for diamonds between 0.14 carats and 0.32 carats, not for any size.

Incorrect. Since there is a significant linear relationship, we can use size to predict price, but only for diamonds between 0.14 carats and 0.32 carats, not for any size.

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Correct. X is size in carats so a one unit increase in X is a one carat increase in size. Slope is a positive 5944.8 so Y, price, increases by $5944.80 for every one carat increase in size on average.

Incorrect. X is size in carats so a one unit increase in X is a one carat increase in size. Slope is a positive 5944.8 so Y, price, increases by $5944.80 for every one carat increase in size on average.

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Correct. This interval estimates the true or theoretical slope.

Incorrect. This interval estimates the true or theoretical slope.

2

Correct. $1407.32 predicts both the price of an individual .25 carat diamond and the mean price of all .25 carat diamonds.

Incorrect. $1407.32 predicts both the price of an individual .25 carat diamond and the mean price of all .25 carat diamonds.

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Correct. ($1375.26, $1439.39) is the confidence interval estimating the mean price of all .25 carat diamonds.

Incorrect. ($1375.26, $1439.39) is the confidence interval estimating the mean price of all .25 carat diamonds.

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Correct. ($1273.88, $1540.77) is the prediction interval estimating the price of an individual .25 carat diamond.

Incorrect. ($1273.88, $1540.77) is the prediction interval estimating the price of an individual .25 carat diamond.

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Correct. We expect all statistical software packages to give the same prediction intervals.

Incorrect. We expect all statistical software packages to give the same prediction intervals.

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