Queston Ser x²-4 Composite Trapezoidal rule with n=4 3.1.1. use the to approximate integral. 3.1.2. Use the composite rule with n=3 to approximate
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- The manufacturer of hardness testing equipment uses steel-ball indenters to penetrate metal that is being tested. However, the manufacturer thinks it would be better to use a diamond indenter so that all types of metal can be tested. Because of differences between the two types of indenters, it is suspected that the two methods will produce different hardness readings. The metal specimens to be tested are large enough so that two indentions can be made. Therefore, the manufacturer uses both indenters on each specimen and compares the hardness readings. Construct a 95% confidence interval to judge whether the two indenters result in different measurements. Note: A normal probability plot and boxplot of the data indicate that the differences are approximately normally distributed with no outliers. LOADING... Click the icon to view the data table.Specimen Steel ball Diamond1 50 522 57 563 61 614 71 745 68 696 54 567 65 688 51 519 53 56 Construct a 95% confidence interval to…Plz answer for the critical value as wellTo test the claim that the resistance of electric wire can be reduced by more than 0.050 ohm by alloying, 25 values obtained for alloyed wire yielded an average of 0.083 ohm with s = 0.003 ohm, and 25 values obtained for standard wire yielded an average of 0.086 ohm with s = 0.002 ohm. Use 5% level f significance to determine whether the claim has been substantiated. What is the computed value and decision?
- Rochelle was curious about the gender ratio in mechanical engineering versus chemical engineering in American universities. She obtained separate random samples of 30 students from each field of study. She found that 5 of the mechanical engineering students in her sample were female, and 10 of the chemical engineering students in her sample were female. She plans to use these results to make a two-sample zzz interval to estimate the difference between the proportion of females in each field of study. Which conditions for constructing this type of interval did Rochelle's samples meet? I. Both samples were randomly selected from their populations. II. The counts of successes and failures are sufficiently large in each sample. III. Individual observations in each sample can be considered independent, and the samples themselves are independent.Type I error occurs when H0 is correct but H0 is rejected. True or False?An industrial product is packaged in batches of units each. The number ofdefective units within each batch is unknown. Since checking whether aunit is defective or not is expensive, the quality control consists in selectingunits of the batch and obtaining an estimation of the number of defectiveunits within the batch. The batch is rejected if the estimated number ofdefective units exceeds . a. Find the moment estimator of the number of defective units within aparcel.b. If N=20, n=5, and among these units 2 of them are defective, is thebatch rejected?
- only define the parameter and write the null and alternative hypotheses The production line for Glow toothpaste is designed to fill tubes with a mean weight of 6 oz.Periodically, a sample of 35 tubes will be selected in order to check the filling process. Qualityassurance procedures call for the continuation of the filling weight for the population of toothpastetubes is 6 ounces; otherwise the processes will be adjusted. Suppose a sample of 35 toothpaste tubesprovides a sample mean of 6.1 oz and standard deviation of 0.2 oz. State the parameter and both hypotheses to help determine whether the filling process should continue operating or be stopped and corrected.Can you please solve the given inital-value problem on the interval (-∞,0) ?The volume of a box is calculated where the measured dimensions are 20 cm, 15 cm and12 cm. The actual values for each dimension can be more or less different to 0.2 cm. Evaluateabsolute, relative and percentage error of the operation considering the maximum errorcondition by rounding-off the error values correct to 5 significant figures.
- PT. X is an industry engaged in concrete steel with various diameter sizes. The product that is mostly produced is concrete iron with a diameter of 12 mm because it suits the needs of consumers and the current pandemic conditions. During the period from January to December 2019, PT. X is capable of producing as many as 6800 tonnes of units. From the results produced, there is a product defect of 70.4 with the type of product damage, namely overfill (wing), overlap (excessive shape), underfill (kempong) and scratch (beret). In that period, defects were found above the tolerance limit of 2%, namely at week 5 and week 12 of 2.42% and 2.21%. During the production process PT.X has a 2% probability of producing defective products. If you check is 065, then determine:a. P(X=0)b. P(X=1)c. P(X=2)d. P(X≤2)e. P(X≥3)State the hypothesis and identify the claim. Find the critical and z-values.Solve for average value of the function within interval [0,20]