Probability and Statistics for Engineering and the Sciences
9th Edition
ISBN: 9781305251809
Author: Jay L. Devore
Publisher: Cengage Learning
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Chapter 15.3, Problem 21E
To determine
Find the 90% rank-sum confidence interval for
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An experiment to compare the tension bond strength of polymer latex modified mortar (Portland cement mortar to which polymer latex emulsions have been added during mixing) to that of unmodified mortar resulted in x = 18.19 kgf/cm? for the
modified mortar (m = 42) and y = 16.85 kgf/cm? for the unmodified mortar (n = 30). Let u, and u, be the true average tension bond strengths for the modified and unmodified mortars, respectively. Assume that the bond strength distributions are both
normal.
Assuming that o, = 1.6 and o, = 1.3, test Hn: 4, - H, = 0 versus H: u, - u, > 0 at level 0.01.
Calculate the test statistic and determine the P-value. (Round your test statistic to two decimal places and your P-value to four decimal places.)
P-value =
Compute the probability of a type II error for the test of part (a) when 4 - Hz = 1. (Round your answer to four decimal places.)
Suppose the investigator decided to use a level 0.05 test and vwished B = 0.10 when u, - uz = 1. If m = 42, what value of n…
An experiment to compare the tension bond strength of polymer latex modified mortar (Portland cement mortar to which polymer latex emulsións have been added during mixing) to that of
unmodified mortar resulted in x = 18.11 kgf/cm2 for the modified mortar (m = 42) and y = 16.88 kgf/cm2 for the unmodified mortar (n = 31). Let ₁ and ₂ be the true average tension bond
strengths for the modified and unmodified mortars, respectively. Assume that the bond strength distributions are both normal.
(a) Assuming that o₁ = 1.6 and ₂ = 1.3, test Ho: ₁ - ₂ = 0 versus H₂: H₁ - H₂> 0 at level 0.01.
Calculate the test statistic and determine the P-value. (Round your test statistic to two decimal places and your P-value to four decimal places.)
Z =
P-value =
State the conclusion in the problem context.
O Fail to reject Ho. The data suggests that the difference in average tension bond strengths exceeds 0.
Fail to reject Ho. The data does not suggest that the difference in average tension bond strengths…
An experiment to compare the tension bond strength of polymer latex modified mortar (Portland cement mortar to which polymer latex emulsions have been added during mixing) to that of unmodified mortar resulted in x = 18.18 kgf/cm² for the modified mortar (m = 42) and y = 16.86 kgf/cm²
for the unmodified mortar (n = 30). Let µ1 and uz be the true average tension bond strengths for the modified and unmodified mortars, respectively. Assume that the bond strength distributions are both normal.
(a) Assuming that o1 = 1.6 and o2 = 1.3, test Ho: H1 - 42 = 0 versus Ha: H1 - H2 > 0 at level 0.01.
Calculate the test statistic and determine the P-value. (Round your test statistic to two decimal places and your P-value to four decimal places.)
Z = 3.854
P-value = 0.0001
State the conclusion in the problem context.
Fail to reject Ho. The data does not suggest that the difference in average tension bond strengths exceeds from 0.
Reject Ho. The data does not suggest that the difference in average…
Chapter 15 Solutions
Probability and Statistics for Engineering and the Sciences
Ch. 15.1 - Give as much information as you can about the...Ch. 15.1 - Here again is the data on expense ratio (%) for a...Ch. 15.1 - The accompanying data is a subset of the data...Ch. 15.1 - A random sample of 15 automobile mechanics...Ch. 15.1 - Both a gravimetric and a spectrophotometric method...Ch. 15.1 - Reconsider the situation described in Exercise 39...Ch. 15.1 - Use the large-sample version of the Wilcoxon test...Ch. 15.1 - Reconsider the port alcohol content data from...Ch. 15.1 - Prob. 9ECh. 15.2 - Prob. 10E
Ch. 15.2 - Prob. 11ECh. 15.2 - The article A Study of Wood Stove Particulate...Ch. 15.2 - The urinary fluoride concentration (parts per...Ch. 15.2 - Prob. 14ECh. 15.2 - The article Measuring the Exposure of Infants to...Ch. 15.2 - Prob. 16ECh. 15.3 - Prob. 17ECh. 15.3 - Compute the 99% signed-rank interval for true...Ch. 15.3 - Prob. 19ECh. 15.3 - Prob. 20ECh. 15.3 - Prob. 21ECh. 15.3 - Compute a 99% CI for 1 2 using the data in...Ch. 15.4 - The accompanying data refers to concentration of...Ch. 15.4 - Prob. 24ECh. 15.4 - Prob. 25ECh. 15.4 - Prob. 26ECh. 15.4 - In an experiment to study the way in which...Ch. 15 - The article Effects of a Rice-Rich Versus...Ch. 15 - Prob. 29SECh. 15 - The given data on phosphorus concentration in...Ch. 15 - Prob. 31SECh. 15 - Prob. 32SECh. 15 - The sign test is a very simple procedure for...Ch. 15 - Prob. 34SECh. 15 - Prob. 35SECh. 15 - Prob. 36SE
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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_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: 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…arrow_forward
- 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…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: 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…arrow_forwardAn experiment to compare the tension bond strength of polymer latex modified mortar (Portland cement mortar to which polymer latex emulsions have been added during mixing) to that of unmodified mortar resulted in x = 18.18 kgf/cm² for the modified mortar (m = 42) and y = 16.85 kgf/cm² for the unmodified mortar (n = 32). Let μ₁ and ₂ be the true average tension bond strengths for the modified and unmodified mortars, respectively. Assume that the bond strength distributions are both normal. (a) Assuming that 0₁ = 1.6 and ₂ = 1.3, test Ho: M₁ M₂ = 0 versus Ha: M₁ M₂ > 0 at level 0.01. 1 Calculate the test statistic and determine the P-value. (Round your test statistic to two decimal places and your P-value to four decimal places.) z = 4.74 X P-value = State the conclusion in the problem context. Ⓒ Reject Ho. The data suggests that the difference in average tension bond strengths exceeds 0. O Reject Ho. The data does not suggest that the difference in average tension bond strengths exceeds…arrow_forward
- An experiment to compare the tension bond strength of polymer latex modified mortar (Portland cement mortar to which polymer latex emulsions have been added during mixing) to that of unmodified mortar resulted in x = 18.17 kgf/cm² for the modified mortar (m = 42) and y = 16.82 kgf/cm² for the unmodified mortar (n = 31). Let μ₁ and ₂ be the true average tension bond strengths for the modified and unmodified mortars, respectively. Assume that the bond strength distributions are both normal. (a) Assuming that 0₁ = 1.6 and 0₂ = 1.3, test Ho: M₁ M₂ = 0 versus Ha: M₁ - H₂> 0 at level 0.01. Calculate the test statistic and determine the P-value. (Round your test statistic to two decimal places and your P-value to four decimal places.) Z P-value = (b) Compute the probability of a type Il error for the test of part (a) when µ₁ - H₂ = 1. (Round your answer to four decimal places.) (c) Suppose the investigator decided to use a level 0.05 test and wished B = 0.10 when M₁ M₂ = 1. If m = 42, what…arrow_forwardAn experiment to compare the tension bond strength of polymer latex modified mortar (Portland cement mortar to which polymer latex emulsions have been added during mixing) to that of unmodified mortar resulted in x = 18.18 kgf/cm2 for the modified mortar (m = 42) and y = 16.86 kgf/cm for the unmodified mortar (n = 30). Let µ1 and Hz be the true average tension bond strengths for the modified and unmodified mortars, respectively. Assume that the bond strength distributions are both normal. (a) Assuming that o1 = 1.6 and o2 = 1.3, test Ho: µ1 - 42 = 0 versus H3: µ1 – 42 > 0 at level 0.01. Calculate the test statistic and determine the P-value. (Round your test statistic to two decimal places and your P-value to four decimal places.) z = P-value = State the conclusion in the problem context. Fail to reject Ho: The data does not suggest that the difference in average tension bond strengths exceeds from 0. o Reject Ho: The data does not suggest that the difference in average tension bond…arrow_forwardAn experiment to compare the tenslon bond strength of polymer latex modified mortar (Portland cement mortar to which polymer latex emulsions have been added during mixing) to that of unmodified mortar resulted in x=10.16 kol/cm for the modified mortar (m = 42) and y= 16.87 kgf/cm for the unmodified mortar (n= 31). Let , and Ha be the true average tension bond strengths for the modified and unmodified mortars, respectively. Assume that the bond strength distributions are both normal. (0) Assuming that o, = 1.6 and a, 13, test H -,- o versus H >0 at level 0.01. Calculate the test statistic and determine the P value. (Round your test statistic to two decimal places and your P-value to four decimal places.) 2=1377 Pvalue=0 0001 State the conclusion in the problem context. Reject H The data suggests that the difference in average tension bond strengths exceeds d. O Fail to reject H The data does not suggest that the difference in average tension bond strengths exceeds from 0. O Reject H The…arrow_forward
- An experiment to compare the tension bond strength of polymer latex modified mortar (Portland cement mortar to which polymer latex emulsions have been added during mixing) to that of unmodified mortar resulted in x = 18.11 kgf/cm² for the modified mortar (m = 42) and y = 16.82 kgf/cm² for the unmodified mortar (n = 30). Let μ₁ and μ₂ be the true average tension bond strengths for the modified and unmodified mortars, respectively. Assume that the bond strength distributions are both normal. (a) Assuming that ₁ = 1.6 and ₂ = 1.3, test Ho: ₁ - ₂ = 0 versus H₂ : ₁ - ₂ > 0 at level 0.01. Calculate the test statistic and determine the P-value. (Round your test statistic to two decimal places and your P-value to four decimal places.) z = P-value = State the conclusion in the problem context. O Reject Ho. The data does not suggest that the difference in average tension bond strengths exceeds 0. O Fail to reject Ho. The data does not suggest that the difference in average tension bond strengths…arrow_forwardAn experiment to compare the tension bond strength of polymer latex modified mortar (Portland cement mortar to which polymer latex emulsions have been added during mixing) to that of unmodified mortar resulted in x = 18.11 kgf/cm² for the modified mortar (m = 42) and y = 16.82 kgf/cm² for the unmodified mortar (n = 32). Let μ₁ and μ₂ be the true average tension bond strengths for the modified and unmodified mortars, respectively. Assume that the bond strength distributions are both normal. (a) Assuming that 0₁ = 1.6 and ₂ = 1.3, test Ho: ₁ - ₂ = 0 versus H₂: M₁-M₂ > 0 at level 0.01. Calculate the test statistic and determine the P-value. (Round your test statistic to two decimal places and your P-value to four decimal places.) z = P-value = State the conclusion in the problem context. O Reject Ho. The data does not suggest that the difference in average tension bond strengths exceeds 0. O Fail to reject Ho. The data suggests that the difference in average tension bond strengths exceeds…arrow_forwardGiven the Z scores of: -1.5, 0.52, -1.0, 1.7 and 3.0: 1. Calculate the raw skewness and kurtosis scores for these data. 2. Calculate the standard error scores for skewness and kurtosis for these data. 3. Calculate the Z scores for skewness and kurtosis for these data.arrow_forward
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