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- A random sample of 18 size AA batteries for toys yield a mean of 2.6 hours with standard deviation, 1.42 hours. (a) Find the critical value, t*, for a 99% CI. t* = (b) Find the margin of error for a 99% CI. =A type of casting iron has Hall-Petch parameters: σ0 = 36.3 MPa and K = 6.5 MPa ∙ mm^−0.5. For a given sample, the grain size distribution is shown in the diagram below. Each bar represents the percentage of grains in particular size. First, estimate the average grain size based on concept of “weighted mean” (in case you do not know, search for this term). Then, apply Hall-Petch Equation to calculate the yield stress. (Note: 1 μm = 0.001 mm)The gasoline consumption projected for a car model is 13 km / l. After the launch of the vehicle, a specialized magazine carried out a test that showed 1300 cars, an average consumption of 12.3 km / l. The manufacturer claims that the standard deviation of consumption is 0.5 km / l. test the hypothesis that consumption is at least 13km / l.
- The blood pressure (average of systolic and diastolic measurements) of each of 25 randomly selected persons was measured. The average was 97.5 mm Hg, and the standard deviation was 8.05 mm Hg. What is the critical t value? What is the margin of error?Assume that ui and µ2 are the averages of maximum speeds of new high-tech electric scooter types. Use the t test at significance level 0.01 to test Ho: µi - µ2 = -18 versus H.: μι - μ2<18 for the following data: ni = 6, x1=117.8, si=5.06, n2 = 6, xz= 128.2, and s2 = 5.28. (where n, , and s denote the sample size, sample mean and sample standard deviation respectively.) %3DThe average number of miles a person drives per day is 24. A researcher wishes to see if people over age 60 drive less than 24 miles per day. She selects a random sample of 40 drivers over the age of 60 and finds that the mean number of miles driven is 22.7. The population standard deviation is 2.9 miles. At =α0.01, is there sufficient evidence that those drivers over 60 years old drive less than 24 miles per day on average? Assume that the variable is normally distributed. Use the critical value method with tables. State the hypotheses and identify the claim with the correct hypothesis.
- 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 mLAssume that the helium porosity (in percentage) of coal samples taken from any particular seam is normally distributed with true standard deviation A. Compute a 98% CI for true average porosity of another seam based on n specimens with a sample average porosity of B. n=21 B=5.1 A=0.8 What is the upper bound? Two decimal placesSuppose that the average life of a refrigerator before replacement is μ = 15 years with a (68%of data) range from 13 to 17 years. Let x = age at which a refrigerator is replaced. Assumethat x has a distribution that is approximately normal. Find a good approximation for thestandard deviation of x values.