1. A process has demonstrated that, when held in control, it can maintain a o of 0.15 cm. A certain part has specifications of 15.00 ± 0.50 cm. (c) What is the probability that any value of X will fall within the control limits (the probability of Type II error)? (d) Test the natural process spread (60) against the specification range. Is this process capable?
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- The desired percentage of Sio, in a certain type of aluminous cement is 5.5. To test whether the true average percentage is 5.5 for a particular production facility, 16 independently obtained samples are analyzed. Suppose that the percentage of Sio, in a sample is normally distributed with o = 0.32 and that x = 5.23. (Use a = 0.05.) (a) Does this indicate conclusively that the true average percentage differs from 5.5? State the appropriate null and alternative hypotheses. Ho: u = 5.5 Hg: µ 2 5.5 Ho: H = 5.5 HaiH 5.5 = Calculate the test statistic and determine the 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. Do not reject the null hypothesis. There is not sufficient evidence to conclude that the true average percentage differs from the desired percentage. O Reject the null hypothesis. There is sufficient evidence to conclude that the true average percentage differs from the…A mixture of pulverized fuel ash and Portland cement to be used for grouting should have a compressive strength of more than 1,300 KN/m2. The mixture will not be used unless experimental evidence indicates conclusively that the strength specification has been met. Suppose compressive strength for specimens of this mixture is normally distributed with σ = 61. Let μ denote the true average compressive strength. For a test with α = 0.01, what is the probability that the mixture will be judged unsatisfactory when in fact μ = 1,350 (a type II error)? (Round your answer to four decimal places.)Past research has indicated that the average age of death row inmates is 41 years old. researcher would like to determine if the average age has changed. She randomly selects 50 death row inma s and ds their average age to be 37 years old. The hypothesis the statistician wants to test is: a. Ho: µ=37 vs_ Ha: µ ± 41. b. Ho: µ=41 vs Ha: µ< 41. Ho: u = 41 vs. H: u 41 d. Ho: µ=37 vs_Ha: µ< 41. C. 2. If a player at a casino is playing roulette and betting on red, there is a 18 / 38 or 0.474 chance that he will win on any spin of the roulette wheel. If we take a random sample of 300 players betting on red, then p is the proportion of times that the player wins. What is the mean of the sampling distribution of p? t' a. b. What is the standard deviation (os) of the sampling distribution of p? c. If repeated samples of 300 players are taken, what would be the range of the sample proportion of players victories according to the 95 part of the 68-95-99.7 rule" pts) 3. The z statistic for a…
- To test Ho: o=2.3 versus H1:0> 2.3, a random sample of size n= 15 is obtained from a population that is known to be normally distributed. Cormplete parts (a) through (d). (a) If the sample standard deviation is determined to be s=2.1, compute the test statistic. xổ =(Round to three decimal places as needed.) %3D (b) If the researcher decides to test this hypothesis at the a= 0.05 level of significance, determine the critical value. xo 05 = (Round to three decimal places as needed.) (c) Draw a chi-square distribution and depict the critical region. 11.67 23.69 6.571 23.685 11.67 23.69 (d) Will the researcher reject the null hypothesis? Click to select your answer(s). ChpA company claims that the mean monthly residential electricity consumption in a certain region is more than 860 kiloWatt-hours (kWh). You want to test this claim. You find that a random sample of 69 residential customers has a mean monthly consumption of 880 kWh. Assume the population standard deviation is 126 kWh. At α=0.01, can you support the claim? Complete parts (a) through (e). Also find the critical values.Suppose in a local Kindergarten through 12th grade (K -12) school district, 49% of the population favor a charter school for grades K through 5. A simple random sample of 144 is surveyed. a. Find the mean and the standard deviation of X of B(144, 0.49). Round off to 4 decimal places. O = b. Now approximate X of B(144, 0.49) using the normal approximation with the random variable Y and the table. Round off to 4 decimal places. Y - N( c. Find the probability that at most 81 favor a charter school using the normal approximation and the table. (Round off to z-values up to 2 decimal places.) P(X 75) - P(Y > a (Z > e. Find the probability that exactly 81 favor a charter school using the normal approximation and the table. (Round off to z-values up to 2 decimal places.) P(X = 81) - P(The pressure of air (in MPa) entering a compressor is measured to be X = 8.5 ± 0.2, and the pressure of the air leaving the compressor is measured to be Y = 21.2 ± 0.3. The intermediate pressure is therefore measured to be P = √XY = 13.42 . Assume that X and Y come from normal populations and are unbiased. a) From what distributions is it appropriate to simulate values X* and Y*? b) Generate simulated samples of values X*, Y*, and P*. c) Use the simulated sample to estimate the standard deviation of P. d) Construct a normal probability plot for the values P*. Is it reasonable to assume that P is approximately normally distributed? e) If appropriate, use the normal curve to find a 95% confidence interval for the intermediate pressure.Suppose in a local Kindergarten through 12th grade (K -12) school district, 49% of the population favor a charter school for grades K through 5. A simple random sample of 144 is surveyed. a. Find the mean and the standard deviation of X of B(144, 0.49). Round off to 4 decimal places. O = b. Now approximate X of B(144, 0.49) using the normal approximation with the random variable Y and the table. Round off to 4 decimal places. Y - N( c. Find the probability that at most 81 favor a charter school using the normal approximation and the table. (Round off to z-values up to 2 decimal places.) P(X 75) - P(Y > a (Z > e. Find the probability that exactly 81 favor a charter school using the normal approximation and the table. (Round off to z-values up to 2 decimal places.) P(X = 81) - P(A company claims that the mean monthly residential electricity consumption in a certain region is more than 860 kilo Watt-hours (kWh). You want to test this claim. You find that a random sample of 69 residential customers has a mean monthly consumption of 890 kWh. Assume the population standard deviation is 123 kWh. At α=0.05, can you support the claim? Complete parts (a) through (e). (b) Find the critical value(s) and identify the rejection region(s). Select the correct choice below and fill in the answer box within your choice. Use technology. (Round to two decimal places as needed.) A. The critical values are ±enter your response here. B. The critical value is enter your response here.The random variable x has a normal distribution with mean 50 and variance 9. Find the value of x, call it x0, such that: a) P(x ≤ xo) = 0.8413 b) P(x > xo) = 0.025 c) P(x > xo) = 0.95 d) P(41 ≤ x ≤ xo) = 0.8630Please solveTo test Ho: o=2.4 versus H₁: o>2.4, a random sample of size n = 16 is obtained from a population that is known to be normally distributed. Complete parts (a) through (d). CIER (a) If the sample standard deviation is determined to be s=2.2, compute the test statistic. x 12.604 (Round to three decimal places as needed.) (b) If the researcher decides to test this hypothesis at the a= 0.01 level of significance, determine the critical value. X.01 (Round to three decimal places as needed.) 4 Check answer Help me solve this View an example Get more help. a 3:55 PM 6/18/2022 O Ei = Type here to search G B K ? Clear all 96°F Mostly sunnySEE MORE QUESTIONSRecommended textbooks for youA First Course in Probability (10th Edition)ProbabilityISBN:9780134753119Author:Sheldon RossPublisher:PEARSON
A First Course in Probability (10th Edition)ProbabilityISBN:9780134753119Author:Sheldon RossPublisher:PEARSON