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ISBN: 9781305779372
Author: Jay L. Devore
Publisher: Cengage Learning
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Chapter 14.2, Problem 21E
To determine
Explain whether to use one sample t test for testing the hypothesis for the true average ratio.
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A study of the properties of metal plate-connected trusses used for roof support yielded the following observations on axial stiffness index (kips/in.) for plate lengths 4, 6, 8, 10, and 12 in:
4: 333.2 409.5 311.0 326.5 316.8 349.8 309.7
6: 433.1 347.2 361.0 404.5 331.0 348.9 381.7
8: 382.4 366.2 351.0 357.1 409.9 367.3 382.0
10: 350.7 452.9 461.4 433.1 410.6 384.2 362.6
12: 413.4 441.8 419.9 410.7 473.4 441.2 465.8
LUSE SALT
Does variation in plate length have any effect on true average axial stiffness? State the relevant hypotheses using analysis of variance.
O Hoi Hy #fly #Hz" Ha #Hs
H: all five μ's are equal
O Hoi H₂H₂ = H3 = HaHs
H: at least two μ's are unequal
O Hoi H₂ = H₂ = H₂ "HaHs
H: all five μ's are unequal
O Hoi H₂ #4₂ # Hz*H4 *H5
H: at least two μ's are equal
Test the relevant hypotheses using analysis of variance with a = 0.01. Display your results in an ANOVA table. (Round your answers to two decimal places.)
Degrees of Sum of Mean
freedom Squares Squares
Error
Total…
A study of the properties of metal plate-connected trusses used for roof support yielded the following observations on axial stiffness index (kips/in.) for plate lengths 4, 6, 8, 10, and 12 in:
4: 329.2 409.5 311.0 326.5 316.8 349.8 309.7
6: 425.1 347.2 361.0 404.5 331.0 348.9 381.7
8: 389.4 366.2 351.0 357.1 409.9 367.3 382.0
10: 341.7 452.9 461.4 433.1 410.6 384.2 362.6
12: 414.4 441.8 419.9 410.7 473.4 441.2 465.8
USE SALT
Does variation in plate length have any effect on true average axial stiffness? State the relevant hypotheses using analysis of variance.
O Ho: M₁ = H₂ = 13 = H4 = 1₂
H₂: all five μ's are unequal
O Ho: My H₂ H3 ‡ M4 # M5
H₂: at least two μ's are equal
O Ho: My # H₂ H3 # H4 # H5
H₂: all five us are equal
=
=
o Hỏi khi là không = 3 = Mà khô
H₂: at least two μ's are unequal
Test the relevant hypotheses using analysis of variance with a = 0.01. Display your results in an ANOVA table. (Round your answers to two decimal places.)
Sum of
Squares
Source
Treatments
Error…
A study of the properties of metal plate-connected trusses used for roof support yielded the following observations on axial stiffness index (kips/in.) for plate lengths 4, 6, 8, 10, and 12 in:
4: 321.2 409.5 311.0 326.5 316.8 349.8 309.7
6: 439.1 347.2 361.0 404.5 331.0 348.9 381.7
8: 390.4 366.2 351.0 357.1 409.9 367.3 382.0
10: 362.7 452.9 461.4 433.1 410.6 384.2 362.6
12: 402.4 441.8 419.9 410.7 473.4 441.2 465.8
USE SALT
Does variation in plate length have any effect on true average axial stiffness? State the relevant hypotheses using analysis of variance.
○ Ho: H₁ = H₂ = H3 = H4=H5
Ha: all five u's are unequal
O Ho: H₁ H₂ H3 H4 H5
Ha: all five μ's are equal
Ho H₁ = ₂ = 3 = H4 = 5
H₂: at least two μ's are unequal
Ho: H₁ H₂ H3 H4 H5
Ha: at least two μ's are equal
Test the relevant hypotheses using analysis of variance with a = 0.01. Display your results in an ANOVA table. (Round your answers to two decimal places.)
Mean
Degrees of Sum of
freedom Squares Squares
Source
Treatments…
Chapter 14 Solutions
Bundle: Probability and Statistics for Engineering and the Sciences, 9th + WebAssign Printed Access Card for Devore's Probability and Statistics for ... and the Sciences, 9th Edition, Single-Term
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- A study of the properties of metal plate-connected trusses used for roof support yielded the following observations on axial stiffness index (kips/in.) for plate lengths 4, 6, 8, 10, and 12 in: 4: 323.2 409.5 311.0 326.5 316.8 349.8 309.7 6: 423.1 347.2 361.0 404.5 331.0 348.9 381.7 8: 393.4 366.2 351.0 357.1 409.9 367.3 382.0 10: 362.7 452.9 461.4 433.1 410.6 384.2 362.6 12: 418.4 441.8 419.9 410.7 473.4 441.2 465.8 Does variation in plate length have any effect on true average axial stiffness? State the relevant hypotheses using analysis of variance. H0: ?1 ≠ ?2 ≠ ?3 ≠ ?4 ≠ ?5Ha: at least two ?i's are equalH0: ?1 = ?2 = ?3 = ?4 = ?5Ha: all five ?i's are unequal H0: ?1 = ?2 = ?3 = ?4 = ?5Ha: at least two ?i's are unequalH0: ?1 ≠ ?2 ≠ ?3 ≠ ?4 ≠ ?5Ha: all five ?i's are equal Test the relevant hypotheses using analysis of variance with ? = 0.01. Display your results in an ANOVA table. (Round your answers to two decimal places.) Source Degrees offreedom Sum…arrow_forwardA study of the properties of metal plate-connected trusses used for roof support yielded the following observations on axial stiffness index (kips/in.) for plate lengths 4, 6, 8, 10, and 12 in: 4: 315.2 409.5 311.0 326.5 316.8 349.8 309.7 6: 405.1 347.2 361.0 404.5 331.0 348.9 381.7 8: 399.4 366.2 351.0 357.1 409.9 367.3 382.0 10: 353.7 452.9 461.4 433.1 410.6 384.2 362.6 12: 417.4 441.8 419.9 410.7 473.4 441.2 465.8 n USE SALT Does variation in plate length have any effect on true average axial stiffness? State the relevant hypotheses using analysis of variance. O Ho: H1# H2 # Hz# H4# H5 H: at least two µ's are equal O Ho: H1 = H2 = H3= H4= H5 H: at least two u's are unequal O Ho: H1 # H2 # Hz# H4# Hs H: all five u's are equal O Ho: H1 = H2 = Hz3 = H4= Hs H: all five u,'s are unequal Test the relevant hypotheses using analysis of variance with a = 0.01. Display your results in an ANOVA table. (Round your answers to two decimal places.) Degrees of freedom Sum of Squares Mean Source…arrow_forwardSeveral 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 1 2 3 4 5 6 7 8 9 10 11 12 13 14 Direct 21 33 0 60 20 61 40 8 13 93 1 68 77 21 Stratified 8 37 8 57 53 61 28 8 8 100 0 57 68 53 Specimen 15 Find the test statistic. (Round your answer to two decimal places.) t = 16 17 18 19 20 21 22 23 24 25 26 27 Direct Find the df. (Round your answer down to the nearest whole number.) df = 33 0 37 17 93 1 40 21 0 8 13 Use technology to find the P-value. (Round your answer to four decimal places.) P-value = 17 40 Stratified 28 0 37 13 93 13 48 21 0 13 40 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 a = 0.05. (Use direct stratified.) 13 77arrow_forward
- ONLY THE LAST ONE Consider the accompanying data on flexural strength (MPa) for concrete beams of a certain type. 5.9 7.2 7.3 6.3 8.1 6.8 7.0 7.5 6.8 6.5 7.0 6.3 7.9 9.0 8.4 8.7 7.8 9.7 7.4 7.7 9.7 8.2 7.7 11.6 11.3 11.8 10.7 The data below give accompanying strength observations for cylinders. 6.5 5.8 7.8 7.1 7.2 9.2 6.6 8.3 7.0 8.3 7.8 8.1 7.4 8.5 8.9 9.8 9.7 14.1 12.6 11.9 Prior to obtaining data, denote the beam strengths by X1, . . . , Xm and the cylinder strengths by Y1, . . . , Yn. Suppose that the Xi's constitute a random sample from a distribution with mean μ1 and standard deviation σ1 and that the Yi's form a random sample (independent of the Xi's) from another distribution with mean μ2 and standard deviation σ2. (a) Use rules of expected value to show that X − Y is an unbiased estimator of μ1 − μ2. E(X − Y) = E(X) − E(Y) = μ1 − μ2 E(X − Y) = E(X) − E(Y) 2 = μ1 − μ2 E(X − Y) = nm E(X) − E(Y) = μ1 − μ2 E(X −…arrow_forwardA statistical program is recommended. 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 1.50 120 2 glass 6.2 2.90 2.70 1.07 140 3 glass 8.5 2.15 2.00 1.98 175 4 glass 10.4 2.90 2.60 1.79 290 5 plastic 8.0 3.20 3.15 1.25 334 6 glass 8.7 2.00 1.80 2.17 87 7 glass 10.2 1.60 1.50 3.19 118 8 plastic 10.5 4.80 3.80 1.09 520 9 plastic 3.4 5.90 5.00 0.29 333 10 plastic 6.9 5.80 4.75 0.59 568 11 tin 10.9 2.90 2.80 1.88 337 12 plastic 9.7 2.45 2.10 1.98 173 13 glass 10.1 2.60 2.20 1.94 245 14 glass 13.0 2.60 2.60 2.50 238 15 glass 13.0 2.70 2.60 2.41 359 16 glass 11.0 3.10 2.90 1.77 305 17 cardboard 8.7 5.10 5.10 0.85 636 18 cardboard 17.1 10.20 10.20 0.84 1255 19 glass 16.5 3.50 3.50 2.36 649 20 glass 16.5 2.70 1.20 3.06 304 21 glass 9.7 3.00 1.70 1.62 310 22 glass 17.8 2.70 1.75 3.30 309 23 glass 14.0 2.50…arrow_forwardValues of modulus of elasticity (MOE, the ratio of stress, i.e., force per unit area, to strain, i.e., deformation per unit length, in GPa) and flexural strength (a measure of the ability to resist failure in bending, in MPa) were determined for a sample of concrete beams of a certain type, resulting in the following data: MOE 29.7 33.1 33.6 35.2 35.4 36.2 36.2 36.3 37.4 37.8 Strength 5.8 7.1 7.2 6.2 8.0 6.9 7.1 7.7 6.7 6.4 MOE 38.6 38.7 39.7 40.9 42.7 42.7 43.6 45.7 45.9 46.8 Strength 7.1 6.4 8.0 8.9 8.3 8.8 7.9 9.6 7.3 7.6 MOE 47.9 49.2 51.6 62.7 69.7 79.6 80.1 Strength 9.8 7.7 7.8 11.5 11.4 11.9 10.6 Fitting the simple linear regression model to then = 27 observations on x = modulus of elasticity and y = flexural strength given in the data above resulted in ý = 7.589, s, = 0.180 when x = 40 and ý = 9.749, s, = 0.255 for x = 60. The simple linear regression model also resulted in a value of s = 0.8718.arrow_forward
- Samples of both surface soil and subsoil were taken from eight randomly selected agricultural locations in a particular county. The soil samples were analyzed to determine both surface pH and subsoil pH, with the results shown in the accompanying table. 2. 3. 6. Location Surface pH 6.55 5.98 5.59 6.17 5.92 6.18 6.43 5.68 Subsoil pH 6.78 6.14 5.80 5.91 6.10 6.01 6.18 5.88 a. Compute a 90% confidence interval for the mean differend between surface and subsoil pH for agricultural land in this county. b. What assumptions are necessary for the interval in Part (a) to be valid?arrow_forwardAn experiment was conducted to study the extrusion process of biodegradable packaging foam. Two of the factors considered for their effect on the unit density (mg/ml) were the die temperature (145 °C vs. 155 °C) and the die diameter (3 mm vs. 4 mm). The results are stored in [Packaging Foam 1]. Source: Data extracted from W. Y. Koh, K. M. Eskridge, and M. A. Hanna, "Supersaturated Split-Plot Designs," Journal of Quality Technology, 45, January 2013, pp. 61-72.At the 0.05 level of significance, 3mm 4mm 57.22 145 72.54 145 53.60 66.70 145 48.13 49.28 145 69.89 44.14 145 62.78 58.37 145 55.18 53.98 155 57.50 63.03 155 54.17 46.73 155 73.86 60.17 155 90.28 46.78 155 88.19 43.27 155 82.61 56.93 Die Temperature a. is there an interaction between die temperature and die diameter? b. is there an effect due to die temperature? c. is there an effect due to die diameter? d. Plot the mean unit density for each die temperature for each die diameter. e. What can you conclude about the effect of die…arrow_forwardValues of modulus of elasticity (MOE, the ratio of stress, i.e., force per unit area, to strain, i.e., deformation per unit length, in GPa) and flexural strength (a measure of the ability to resist failure in bending, in MPa) were determined for a sample of concrete beams of a certain type, resulting in the following data: MOE 29.7 33.1 33.6 35.2 35.4 36.2 36.2 36.3 37.4 37.8 Strength 5.8 7.1 7.2 6.2 8.0 6.9 7.1 7.7 6.7 6.4 МОЕ 38.6 38.7 39.7 40.9 42.7 42.7 43.6 45.7 45.9 46.8 Strength 7.1 6.4 8.0 8.9 8.3 8.8 7.9 9.6 7.3 7.6 МОЕ 47.9 49.2 51.6 62.7 69.7 79.6 80.1 Strength 9.8 7.7 7.8 11.5 11.4 11.9 10.6 Fitting the simple linear regression model to the n = 27 observations on x = modulus of elasticity and y = flexural strength given in the data above resulted in ý = 7.589, s, = 0.180 when x = 40 and ý = 9.749, s, = 0.255 for x = 60. The simple linear regression model also resulted in a value of s = 0.8718. (a) Explain why s, is larger when x = 60 than when x = 40. O The closer x is to…arrow_forward
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