Use a statistical software package to construct a normal
13. Allowable mechanical properties for structural design of metallic aerospace vehicles requires an approved method for statistically analyzing empirical test data. The article “Establishing Mechanical Property Allowable for Metals’’ (J. of Testing and Evaluation, 1998: 293-299) used the accompanying data on tensile ultimate strength (ksi) as a basis for addressing the difficulties in developing such a method.
122.2 | 124.2 | 124.3 | 125.6 | 126.3 | 126.5 | 126.5 | 127.2 | 127.3 |
127.5 | 127.9 | 128.6 | 128.8 | 129.0 | 129.2 | 129.4 | 129.6 | 130.2 |
130.4 | 130.8 | 131.3 | 131.4 | 131.4 | 131.5 | 131.6 | 131.6 | 131.8 |
131.8 | 132.3 | 132.4 | 132.4 | 132.5 | 132.5 | 132.5 | 132.5 | 132.6 |
132.7 | 132.9 | 133.0 | 133.1 | 133.1 | 133.1 | 133.1 | 133.2 | 133.2 |
133.2 | 133.3 | 133.3 | 133.5 | 133.5 | 133.5 | 133.8 | 133.9 | 134.0 |
134.0 | 134.0 | 134.0 | 134.1 | 134.2 | 134.3 | 134.4 | 134.4 | 134.6 |
134.7 | 134.7 | 134.7 | 134.8 | 134.8 | 134.8 | 134.9 | 134.9 | 135.2 |
135.2 | 135.2 | 135.3 | 135.3 | 135.4 | 135.5 | 135.5 | 135.6 | 135.6 |
135.7 | 135.8 | 135.8 | 135.8 | 135.8 | 135.8 | 135.9 | 135.9 | 135.9 |
135.9 | 136.0 | 136.0 | 136.1 | 136.2 | 136.2 | 136.3 | 136.4 | 136.4 |
136.6 | 136.8 | 136.9 | 136.9 | 137.0 | 137.1 | 137.2 | 137.6 | 137.6 |
137.8 | 137.8 | 137.8 | 137.9 | 137.9 | 138.2 | 138.2 | 138.3 | 138.3 |
138.4 | 138.4 | 138.4 | 138.5 | 138.5 | 138.6 | 138.7 | 138.7 | 139.0 |
139.1 | 139.5 | 139.6 | 139.8 | 139.8 | 140.0 | 140.0 | 140.7 | 140.7 |
140.9 | 140.9 | 141.2 | 141.4 | 141.5 | 141.6 | 142.9 | 143.4 | 143.5 |
143.6 | 143.8 | 143.8 | 143.9 | 144.1 | 144.5 | 144.5 | 147.7 | 147.7 |
a. Construct a stem-and-leaf display of the data by first deleting (truncating) the tenths digit and then repeating each stem value five times (once for leaves 1 and 2, a second time for leaves 3 and 4, etc.). Why is it relatively easy to identify a representative strength value?
b. Construct a histogram using equal-width classes with the first class having a lower limit of 122 and an upper limit of 124. Then comment on any interesting features of the histogram.
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Chapter 4 Solutions
Student Solutions Manual for Devore's Probability and Statistics for Engineering and the Sciences, 9th
- Warming and Ice Melt The average depth of the Hudson Bay is 305 feet. Climatologists were interested in seeing if the effects of warming and ice melt were affecting the water level. Fifty-five measurements over a period of weeks yielded a sample mean of 306.2 feet. The population variance is known to be 3.6. Can it be concluded that the average depth has increased with a=.05 ? a)Use the P-value Method b) Use the Critical Value Methodarrow_forwardPhysical properties of six flame-retardant fabric samples were investigated in an article. Use the accompanying data and a 0.05 significance level to determine whether a linear relationship exists between stiffness x (mg-cm) and thickness y (mm). O Ho: P = 0 H₂: P = 0 O Ho: P = 0 H₂:p>0 State the appropriate null and alternative hypotheses. O Ho: P = 0 Ha: P < 0 O Ho: P = 0 Ha: P = 0 X y r = 7.95 24.63 12.39 7.06 24.17 35.70 0.25 0.64 0.32 0.27 0.80 0.56 Compute the value of the sample correlation coefficient, r. Round your answer to four decimal places. Calculate the test statistic and determine the P-value. (Round your test statistic to two decimal places and your P-value to three decimal places.) t = P-value = State the conclusion in the problem context. O Fail to reject Ho. The data does not indicate that the population correlation coefficient differs from 0. O Reject Ho. The data indicates that the population correlation coefficient differs from 0. O Reject Ho. The data does not…arrow_forwardAllowable mechanical properties for structural designof metallic aerospace vehicles requires an approvedmethod for statistically analyzing empirical test data.The article “Establishing Mechanical PropertyAllowables for Metals” (J. of Testing and Evaluation,1998: 293–299) used the accompanying data on tensileultimate strength (ksi) as a basis for addressingthe difficulties in developing such a method.122.2 124.2 124.3 125.6 126.3 126.5 126.5 127.2 127.3127.5 127.9 128.6 128.8 129.0 129.2 129.4 129.6 130.2130.4 130.8 131.3 131.4 131.4 131.5 131.6 131.6 131.8131.8 132.3 132.4 132.4 132.5 132.5 132.5 132.5 132.6132.7 132.9 133.0 133.1 133.1 133.1 133.1 133.2 133.2133.2 133.3 133.3 133.5 133.5 133.5 133.8 133.9 134.0134.0 134.0 134.0 134.1 134.2 134.3 134.4 134.4 134.6134.7 134.7 134.7 134.8 134.8 134.8 134.9 134.9 135.2135.2 135.2 135.3 135.3 135.4 135.5 135.5 135.6 135.6135.7 135.8 135.8 135.8 135.8 135.8 135.9 135.9 135.9135.9 136.0 136.0 136.1 136.2 136.2 136.3 136.4 136.4136.6 136.8…arrow_forward
- Allowable mechanical properties for structural designof metallic aerospace vehicles requires an approvedmethod for statistically analyzing empirical test data.The article “Establishing Mechanical PropertyAllowables for Metals” (J. of Testing and Evaluation,1998: 293–299) used the accompanying data on tensileultimate strength (ksi) as a basis for addressingthe difficulties in developing such a method. 122.2 124.2 124.3 125.6 126.3 126.5 126.5 127.2 127.3127.5 127.9 128.6 128.8 129.0 129.2 129.4 129.6 130.2130.4 130.8 131.3 131.4 131.4 131.5 131.6 131.6 131.8131.8 132.3 132.4 132.4 132.5 132.5 132.5 132.5 132.6132.7 132.9 133.0 133.1 133.1 133.1 133.1 133.2 133.2133.2 133.3 133.3 133.5 133.5 133.5 133.8 133.9 134.0134.0 134.0 134.0 134.1 134.2 134.3 134.4 134.4 134.6134.7 134.7 134.7 134.8 134.8 134.8 134.9 134.9 135.2135.2 135.2 135.3 135.3 135.4 135.5 135.5 135.6 135.6135.7 135.8 135.8 135.8 135.8 135.8 135.9 135.9 135.9135.9 136.0 136.0 136.1 136.2 136.2 136.3 136.4 136.4136.6 136.8…arrow_forwardRefer to laserjeans.xlsx to answer the questions below. These real data come from Ondogan, Z., Pamuk, O., Ondogan, E. N., & Ozguney, A. (2005). Improving the appearance of all textile products from clothing to home textile using laser technology. Optics and Laser Technology, 37, 631-637. Researchers sought to test the differences in tensile strength of jeans designed by hand versus those designed with lasers. 1. What type of measurement scale do each of the five variables use? 2. Create histograms for those that are continuous (interval or ratio). How would you describe the shape of these distributions? 3. A textile researcher wants to simplify the strength data by turning this continuous variable into an ordinal variable with 10 equal interval widths. Given that the lowest force resulting in a rip was 860 N, and the greatest force resulting in a rip was 1,450 N, what should the interval widths (also called bins or breaks) be? Fill in the second column of the…arrow_forwardTensile strength tests were carried out on two different grades of wire rod, resulting in the accompanying data. Sample Mean (kg/mm²) Grade AISI 1064 AISI 1078 Sample Size m = 128 n = 128 Ho: M1064 M1078 = -10 Ha: M1064-H1078 ≤ -10 (a) Does the data provide compelling evidence for concluding that true average strength for the 1078 grade exceeds that for the 1064 grade by more than 10 kg/mm²? Test the appropriate hypotheses using a significance level of 0.01. State the relevant hypotheses. O Ho: M1064 M1078 = -10 Ha: M10641078 # -10 Ho: M1064 M1078 = -10 Ha: M1064-H1078 ² -10 Ho: M10641078 = -10 Ha: M10641078 > -10 Sample SD Ho: M1064- 1078 = -10 Ha: M10641078 < -10 x = 104.7 S₁ = 1.1 y = 124.1 S₂ = 2.2 Calculate the test statistic and 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 true average strength for the 1078 grade exceeds…arrow_forward
- 75T: Statistics X zy Section 5.4- QNT/275T: Statistics X 56598163/chapter/5/section/4 for Decision Making home > ence between two population means 5.4.1: Hypothesis test for the difference between two population means. Jump to level 1 The mean voltage and standard deviation of 9 batteries from each manufacturer were measured. The results are summarized in the following table. Manufacturer B Y OF GULFSIDE Check 171 What is the test statistic? Ex: 0.123 + Sample mean voltage (millivolts) 167 Next What type of hypothesis test should be performed? Select MESA 81101 What is the number of degrees of freedom? Ex: 25 Two-tailed z-test Unpaired t-test Population standard deviation(millivolts) Does sufficient evidence exist to support the claim that the voltage of the batteries made by the two manufacturers is different at the a = 0.1 significance level? Select v 2 2 4 hp Select Left-tailed z-test Paired t-test 3 8arrow_forwardidentify the independent variable, the dependant variable and the unit of analysis of the following statement Lin, W. and Zhou, W. (2020). Factors associated with the physical and mental health of drug users participating in community-based drug rehabilitation programs in China. Health and Social Care, 28(2): 584-509.arrow_forwardMinimization of false trends in measurement caused by extraneous variables can be minimized by: A. Randomizing the order of application of the independent variable. B. Repeated measurement of the dependent variables. C. Signal conditioning and recalibration of the test instrument. D. Neglecting controlled parametrization of fundamental features of the test instrument. E. Getting a new replacement of the test instrument.arrow_forward
- Physical properties of six flame-retardant fabric samples were investigated in an article. Use the accompanying data and a 0.05 significance level to determine whether a linear relationship exists between stiffness x (mg-cm) and thickness y (mm). State the appropriate null and alternative hypotheses. O Ho: P = 0 H₂: P 0 O Ho: P #O H₂: p=0 O Ho: P = 0 H₁₂ :P #0 8.07 24.69 12.33 6.85 24.22 35.69 y 0.29 0.65 0.31 0.27 0.80 0.57 Compute the value of the sample correlation coefficient, r. Round your answer to four decimal places. r= Calculate the test statistic and determine the P-value. (Round your test statistic to two decimal places and your P-value to three decimal places.) t = P-value = State the conclusion in the problem context. O Fail to reject Ho. The data does not indicate that the population correlation coefficient differs from 0. Reject Ho. The data does not indicate that the population correlation coefficient differs from 0. Fail to reject Ho. The data indicates that the…arrow_forwardUsing Excel Tablet’s hardness can be represented by its relative density and tensile strength. Studies have indicated that its tensile strength depends on the relative density, regardless of production shifts. Recently, a batch was found to produce cluster of tablets that show low relative density values of 68%, 74.3%, and 80.1%. Based on the current data in April 2022, what is the prediction of the tensile strength for such tablets? Present the requires analysis and comment on the validity of the model that you have used to carry out this prediction.arrow_forwardStructural engineers use wireless sensor networks to monitor the condition of dams and bridges. The article "Statistical Analysis of Vibration Modes of a Suspension Bridge Using Spatially Dense Wireless Sensor Network" (S. Pakzad and G. Fenves, Journal of Structural Engineering, 2009:863-872) desaribes an experiment in which accelerometers were placed on the Golden Gate Bridge for the purpose of estimating vibration modes. For 18 vertical modes, the system was underdamped (damping ratio 1)? Explain why or why not f. e. For what damping ratio would you predict a frequency of 2.0?arrow_forward
- Glencoe Algebra 1, Student Edition, 9780079039897...AlgebraISBN:9780079039897Author:CarterPublisher:McGraw Hill
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