A statistical program is recommended. An article gave the data, shown in the table below, on dimensions of 27 representative food products. Product Material Height 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 glass glass glass glass plastic glass glass plastic plastic plastic tin plastic glass glass glass glass cardboard cardboard glass glass glass glass glass glass plastic tin tin 7.7 6.2 8.5 10.4 OH₂A₁B₂B₂=0 8.0 8.7 10.2 10.5 3.4 6.9 10.9 9.7 10.1 13.0 13.0 11.0 8.7 17.1 16.5 16.5 9.7 17.8 14.0 13.6 27.9 19.5 13.8 Maximum Width 2.50 2.90 OH: at least one of ₁, ₂ or B, is not 0 H₂: A₁-A₂ =B₂ = 0 2.15 OH: A₂ and , are all not 0 H₂: A₁-A₂=₂=0 2.90 3.20 2.00 1.60 4.80 5.90 5.80 2.90 2.45 2.60 2.60 2.70 3.10 5.10 10.20 3.50 2.70 3.00 2.70 2.50 2.40 4.40 7.50 4.25 Minimum Width (c) Carry out a model utility Ftest at a 0.05 significance level. State the null and alternative hypotheses. B₂ =B₂ = 0 OH₂ B₁ H: ₂ and , are all not 0 H: at least one of ₁.₂ or ₂ is not 0 1.80 2.70 2.00 2.60 3.15 1.80 1.50 3.80 5.00 4.75 2.80 2.10 2.20 2.60 2.60 2.90 5.10 10.20 3.50 1.20 1.70 1.75 1.70 1.20 1.20 7.50 4.25 Elongation Volume 1.50 1.07 1.98 1.79 1.25 2.17 3.19 1.09 0.29 0.59 1.88 1.98 1.94 2.50 2.41 1.77 0.85 0.84 2.36 3.06 1.62 3.30 2.80 2.83 (b) Why should we consider adjusted R² instead of R² when evaluating this model? O We should consider the adjusted O We should consider the adjusted O We should consider the adjusted O We should consider the adjusted instead of instead of instead of instead of 3.17 1.30 1.62 130 139 Calculate the test statistic. (Round your answer to two decimal places.) F= Use technology to calculate the P-value. (Round your answer to four decimal places.) P-value= 180 281 332 93 119 515 325 568 339 180 235 239 363 312 631 1248 651 306 320 (a) Fit a multiple regression model for predicting the volume (in ml) of a package based on its minimum width, maximum width, and elongation score. (Round your numerical values to two decimal places. Use x, for minimum width, x, for the maximum width and x, for the elongation score.) ŷ = 310 247 204 1204 2329 731 because it takes into account the number of predictors used in the model. In this case the adjusted is noticeably less than ². because it does not take into account the number of predictors used in the model. In this case the adjusted is noticeably greater than ². because it takes into account the number of predictors used in the model. In this case the adjusted is noticeably greater than ². because it does not take into account the number of predictors used in the model. In this case the adjusted is noticeably less than ². What can you conclude? O Reject H. We have convincing evidence that the multiple regression model is useful and can conclude that at least one of ₁.₂ or ₂ is not 0. O Fail to reject H. We do not have convincing evidence that the multiple regression model is useful and cannot conclude that ₁, ₂ and S, are all not 0. O Fail to reject H. We do not have convincing evidence that the multiple regression model is useful and cannot conclude that at least one of ₁, ₂ or ₂ is not 0. O Reject H. We have convincing evidence that the multiple regression model is useful and can conclude that ₁₂ and , are all not 0.

15. Diameter of Douglas Fir Trees The diameter of the Douglas fir tree is measured at a height of 1.37 meters. The S following data represent the diameter in centimeters of a random sample of 12 Douglas firs in the western Washington Cascades. 156 162 147 173 147 190 130 101 159 113 181 109 Source: L. Winter. "Live Tree and Tree-Ring Records to Reconstruct the Structural Development of an Old-Growth Douglas Fir/Western Hemlock Stand in the Western Washington Cascades." Corvallis, OR: Forest Science Data Bank, 2005. (a) Obtain a point estimate for the mean and standard deviation diameter of a Douglas fir tree in the western Washington Cascades. (b) Because the sample size is small, we must verify that the data come from a population that is normally distributed and that the data do not contain any outliers. The figures show the normal probability plot and boxplot. The correlation between the tree diameters and expected z-scores is 0.982. Use Option 1 or Option 2 to determine if the…

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Several methods of estimating the number of seeds in soil samples have been developed by ecologists. An article gave the accompanying data on the number of seeds detected by the direct method and by the stratified method for 27 soil specimens. Specimen Direct Stratified 1 21 6 2 32 38 3 0 6 4 60 58 5 20 52 6 61 61 7 40 26 8 6 6 9 12 6 10 92 100 11 1 0 12 66 58 13 78 66 14 21 52   Specimen Direct Stratified 15 32 26 16 0 0 17 38 38 18 18 12 19 92 92 20 1 12 21 40 46 22 21 21 23 0 0 24 6 12 25 12 40 26 18 12 27 40 78   Do the data provide sufficient evidence to conclude that the mean number of seeds detected differs for the two methods? Test the relevant hypotheses using  ? = 0.05.  (Use ?direct − ?stratified.) Find the test statistic. (Round your answer to two decimal places.) t =  Find the df. (Round your answer down to the nearest whole number.) df =   Use technology to find the P-value. (Round your answer to four…

An article gave the data, shown in the table below, on dimensions of 27 representative food products. Product Material Height MaximumWidth MinimumWidth Elongation Volume 1 glass 7.7 2.50 1.80 1.50 121 2 glass 6.2 2.90 2.70 1.07 139 3 glass 8.5 2.15 2.00 1.98 178 4 glass 10.4 2.90 2.60 1.79 288 5 plastic 8.0 3.20 3.15 1.25 328 6 glass 8.7 2.00 1.80 2.17 94 7 glass 10.2 1.60 1.50 3.19 115 8 plastic 10.5 4.80 3.80 1.09 517 9 plastic 3.4 5.90 5.00 0.29 332 10 plastic 6.9 5.80 4.75 0.59 567 11 tin 10.9 2.90 2.80 1.88 340 12 plastic 9.7 2.45 2.10 1.98 177 13 glass 10.1 2.60 2.20 1.94 236 14 glass 13.0 2.60 2.60 2.50 237 15 glass 13.0 2.70 2.60 2.41 358 16 glass 11.0 3.10 2.90 1.77 314 17 cardboard 8.7 5.10 5.10 0.85 635 18 cardboard 17.1 10.20 10.20 0.84 1250 19 glass 16.5 3.50 3.50 2.36 651 20 glass 16.5 2.70 1.20 3.06 300 21 glass 9.7 3.00 1.70 1.62 312 22 glass 17.8 2.70 1.75 3.30 303 23 glass 14.0 2.50 1.70 2.80 247 24 glass 13.6 2.40…

The densities of several common metals are shown in the following table. Metal Density (g/cm³) iron 7.87 silver 10.49 lead 11.36 zinc 7.13 aluminum 2.70 For her chemistry lab, Kamila needs to identify three metal samples by density. The data she collected is shown in the following table. The metal samples are all rectangular prisms.