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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Probability and Statistics for Engineering and the Sciences
- 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_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_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_forward
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