An experiment was performed to compare the abrasive wear of two different laminated materials. Twelve pieces of material 1 were tested by exposing each piece to a machine measuring wear. Ten pieces of material 2 were similarly tested. In each case, the depth of wear was observed. The samples of material 1 gave an average (coded) wear of 85 units with a sample standard deviation of 4, while the samples of material 2 gave an average of 81 with a sample standard deviation of 5. Can we conclude at the 0.05 level of significance that the abrasive wear of material 1 exceeds that of material 2 by more than 2 units? Assume the populations to be approximately normal with equal variances.

A researcher compares two compounds (1 and 2) used in the manufacture of car tires that are designed to reduce braking distances for SUVs equipped with the tires. The mean braking distance for SUVs equipped with tires made with compound 1 is 65 feet, with a population standard deviation of 13.6. The mean braking distance for SUVS equipped with tires made with compound 2 is 69 feet, with a population standard deviation of 8.5. Suppose that a sample of 55 braking tests are performed for each compound. Using these results, test the claim that the braking distance for SUVs equipped with tires using compound 1 is shorter than the braking distance when compound 2 is used. Let μ₁ be the true mean braking distance corresponding to compound 1 and μ₂ be the true mean braking distance corresponding to compound 2. Use the 0.05 level of significance. Step 3 of 5 Find the p-value associated with the test statistic. Round your answer to four decimal places. Answer How to enter your answer (opens in…

The void volume within a textile fabric affects comfort, flammability, and insulation properties. Permeability of a fabric refers to the accessibility of void space to the flow of a gas or liquid. An article gave summary information on air permeability (cm3/cm2/sec) for a number of different fabric types. Consider the following data on two different types of plain-weave fabric: Fabric Type Sample Size Sample Mean Sample Standard Deviation Cotton 10 51.41     0.75 Triacetate 10 132.15     3.59 Assuming that the porosity distributions for both types of fabric are normal, let's calculate a confidence interval for the difference between true average porosity for the cotton fabric and that for the acetate fabric, using a 95% confidence level. Before the appropriate t critical value can be selected, df must be determined: df =    0.5625 10  +  12.8881 10   2   (0.5625/10)2 9  +  (12.8881/10)2 9  =  1.8092 0.1849…

A researcher compares two compounds (1 and 2) used in the manufacture of car tires that are designed to reduce braking distances for SUVs equipped with the tires. The mean braking distance for SUVS equipped with tires made with compound 1 is 68 feet, with a population standard deviation of 13.9. The mean braking distance for SUVs equipped with tires made with compound 2 is 73 feet, with a population standard deviation of 13.7. Suppose that a sample of 72 braking tests are performed for each compound. Using these results, test the claim that the braking distance for SUVS equipped with tires using compound 1 is shorter than the braking distance when compound 2 is used. Let μ, be the true mean braking distance corresponding to compound 1 and μ₂ be the true mean braking distance corresponding to compound 2. Use the 0.05 level of significance. Step 1 of 5: State the null and alternative hypotheses for the test.

5. The burning rates of two different solid-fuel propellants used in air crew escape systems are being studied. It is known that both propellants have approximately the same standard deviation of burning rate; that is, o1 =02 = 3 centimeters per second. Two random samples of n1 = 20 and n2 = 20 specimens are tested; the sample mean burning rates are x1 = 18 centimeters per second and x2 = 24 centimeters %3D %3D per second. 5.1. Test the hypothesis that both propellants have the same mean burning rate. Use a=0.05. What is the P-value? 5.2. Construct a 95% confidence interval on the difference in means µ1 -u2. What is the practical meaning of this interval?

A series of measurements in the lab led to an experimental result of 32.9 mL, with a calculated standard deviation of 0.3 mL. What is the standard way to report this result? Select one: 32.6-33.2 mL 32.9 ± 0.3 mL 32.9 ± 0.30 mL = 32.9 mL

In a study of microplastics in our environment, it was determined that there are 5.25 trillion plastic pieces floating in the ocean, weighing more than 250,000 tons. In a recent expedition to examine whether increases in plastic production have led to changes in ocean microplastics, 16 samples were taken at various locations in the Pacific Ocean. It was determined that the average concentration was 9.5 particles per liter of ocean water with a sample standard deviation of 6. In one of the earliest research expeditions to study microplastics in the ocean conducted in 2009, it was determined that the average concentration of microplastics was 6 particles per liter (consider this the population or reference mean). What is the critical value for the two-tailed alternative hypothesis at alpha = 5%? (Hint: This is the value in the table that you will compare your test statistic to in order to determine the outcome of the hypothesis test). 2.131 1.746 2.120 1.753

The slant shear test is widely accepted for evaluating the bond of resinous repair materials to concrete; it utilizes cylinder specimens made of two identical halves bonded at 30°. An article reported that for 12 specimens prepared using wire-brushing, the sample mean shear strength (N/mm2) and sample standard deviation were 18.60 and 1.56, respectively, whereas for 12 hand-chiseled specimens, the corresponding values were 23.19 and 4.07. Does the true average strength appear to be different for the two methods of surface preparation?   State and test the relevant hypotheses using a significance level of 0.05. (Use ?1 for wire-brushing and ?2 for hand-chiseling.) H0: ?1 − ?2 = 0Ha: ?1 − ?2 ≤ 0H0: ?1 − ?2 = 0Ha: ?1 − ?2 < 0    H0: ?1 − ?2 = 0Ha: ?1 − ?2 > 0H0: ?1 − ?2 = 0Ha: ?1 − ?2 ≠ 0 Calculate the test statistic and determine the P-value. (Round your test statistic to one decimal place and your P-value to three decimal places.) t  =    P-value  =   You may have computed…

Acrylic bone cement is sometimes used in hip and knee replacements to fix an artificial joint in place. The force required to break an acrylic bone cement bond was measured for eight specimens under specified conditions, and the resulting mean and standard deviation were 306.11 newtons and 41.94 newtons, respectively. Assuming that it is reasonable to believe that breaking force under these conditions has a distribution that is approximately normal, estimate the mean breaking force for acrylic bone cement under the specified conditions using a 95% confidence interval. (Use a table or technology. Round your answers to three decimal places.) n USE SALT

Following maintenance and calibration, an extrusion machine produces aluminum tubing with a mean outside diameter of 2.500 inches. As the machine functions over an extended number of work shifts the combination accumulated deposits and mechanical wear causes the mean diameter to drift away from the desired 2.500 inches. For a recent random sample of thirty-four tubes, the mean diameter was 2.491 inches and the standard deviation was 0.027 inches. Does the machine appear to be in need of maintenance and calibration (use α = 0.01)? Also, determine the p-value for the test. a. Provide the hypothesis (2 Points) b. Provide the test statistics formula(s) (3 Points) c. Conduct the calculations and provide results (6 Points) d. Discuss the decision of whether or not rejecting the hypothesis (2 Points) e. Discuss the business conclusion (2 Points)