1) APAC's aviation part manufacturer claims that new composite part has a mean shearing strength of less than 3000 kPa. Eight sample composite parts are tested randomly with mean and standard deviation, I = 2959 and s = 39.1. Is there enough evidence to support the manufacturer's claim at %3D 0.025 significance level?
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- 3. Calcium in a mineral was analyzed five times by each of two methods, with similar standard deviations. Are the mean values significantly different at the 95% confidence level? Method X 0.0282 0.0279 0.0271 0.0275 Method Y 0.0271 0.0271 0.0268 0.0263 0.0274 0.0269A consumer group wants to estimate the monthly electricity consumption ofhouseholds in a district. Assume the standard deviation of monthly householdelectricity usage in the district is 40 kwh. What sample size of households shouldbe selected and surveyed to estimate the mean monthly household electricityconsumption to within 15 kwh (margin of error) with 95% confidence?An experiment was performed to compare the abrasive wear of two different coating materials on the cutting tools: • Coating material A: 11 pieces were tested, which gave average wear of 85 units with a sample standard deviation of 4 units. • Coating material B: 10 pieces were tested, which gave average wear of 81 units with a sample standard deviation of 5 units. Assume the populations to be normal. 1) Can we conclude at the 0.05 level of significance that the population variances of material A and material B are different? 2) Can we conclude at the 0.05 level of significance that the abrasive wear of material A exceeds that of material B if the population variances of material A and B are equal?
- 1) Sampling Distribution for Sample Variances a) A cell phone manufacturer wants to advertise their new extended-life batteries. They believe the lifetimes are normally distributed with o = 1.15 hr. A test engineer takes a sample of 10 batteries and calculates a sample standard deviation of 1.3 hr. Can the manufacturer confidently advertise the standard deviation in the lifetime of their new batteries? Use critical values of X1.95 and X3.05 (a 90% window). i) Find the value of the test statistic for this sample and the two critical values. ii) 2 X0.95 = YES x² = Can the manufacturer confidently advertise the standard deviation in the lifetime of their new batteries? Circle YES or NO and briefly explain your answer. NO X0.05 =An avionics company uses a new production method to manufacture aircraft altimeters. A single random sample of new altimeters resulted in the errors listed below. Use a 5% significance level to test the claim that the new production method has errors with a standard deviation greater than 32.2 ft, which was the standard deviation for the old production model (o). If it appears that the standard deviation is greater, does the new production method appear to be better or worse than the old method? Should the company take any action? -42 78 -22 -72 -45 15 17 51 -5 -53 -9 -109 Find the upper and lower boundaries of the 95% confidence interval for o. 98 37 32 73 89A sample of 12 concrete specimens from supplier A were tested for their compressive strength. The results gave an average of 85 MPa and a standard deviation of 4 MPa. From supplier B, 10 specimens were similarly tested and gave an average compressive strength of 81 MPa and a standard deviation of 5 MPa. (a) Using procedures of Hypothesis Testing, can we conclude at the 0.05 level of significance that the compressive strength of concrete from A exceeds that from B by more than 2 MPa? Assume the populations to be approximately normal with equal variances. (b) Is the assumption of equal variances in (a) justifiable at an a = 0.10?
- An article shows data to compare several methods for predicting the shear strength for steel plate girders. Data for two of these methods, the Karlsruhe and Lehigh procedures, when applied nine times to a girder, are shown in the following table. We wish to determine whether there is any difference between the two methods. Assume the same standard deviations. (Note that we will perform unpaired comparison. We do not perform a paired test.) Karlsruhe Method Lehigh Method 1.21304 1.160384 1.251478 1.268834 1.218271 1.214254 1.232497 1.244961 1.142573 1.091621 1.286563 1.2297 1.239222 1.219269 1.161394 1.162844 1.169785 1.118203 1.231058 1.199258 1.233329 1.269486 1.153381 1.106666 1.2. For a sample standard deviation, use Excel function STDEV.S(), not STDEV.P(). Fill in the blanks below: Karlsruhe Method Lehigh Method x1 = x2 = s1 = s2 = n1 = n2 = 1.3. Do the data suggest that the two…Concrete cubes are used to test the quality of mix from a concrete mixing plant. 28 day compressive strength is taken as the standard measure to test the quality of the mix. Tests show that mean compressive strength of a sample of cubes is 28.4 units with a standard deviation of 2.95 units. To assure quality, the mixing company requires that at least 95% of the samples have compressive strength greater than 24 units. Based on this information and assuming a large sample size, answer the following questions. After major improvements on the plant, the mixing company is able to make cubes more consistent (reduce SD of compressive strength but maintain the same mean). For what value of the new SD will be cube standards be just met? Based on the requirements, only about___% of the samples meet the company standards.?The breaking force of the cables produced by a manufacturer is 1800 lbs (lb) and the standard deviation is 100 lbs. It is claimed that the breaking force can be increased with a new technique in the manufacturing process. To test this claim, a sample of 50 wires is taken and tested. The average breaking force of the samples is found as 1850 lb. Can we support this claim at the 0.01 significance level?
- A factory produces tables which are claimed on average to have a length of 150.0 cm. Assume the standard deviation is known to be a = 0.6 cm, and that the length of tables is normally distributed. The factory's manager wants to carry out a test of: Ho : = = 150.0 vs. H₁ < 150.0 at the 10% significance level. Determine the sample size which is necessary for the test to have 99% power if the true mean length is 149.7 cm.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 1.753The specifications for the production of a certain alloy call for 23.2% copper. A sample of 10 analyses of the product showed a mean copper content of 23.5% and a standard deviation of 0.24 %. Can we conclude at 0.01 significance levels that the product meets the required specifications
