The 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
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The specifications for the production of a certain alloy call for 23.2% copper. A sample of 10 analyses of the product showed a
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- A particular manufacturing design requires a shaft with a diameter of 19.000 mm, but shafts with diameters between 18.987 mm and 19.013 mm are acceptable. The manufacturing process yields shafts with diameters normally distributed, with a mean of 19.003 mm and a standard deviation of 0.004 mm.Complete parts (a) through(d) below. For this process, what is the proportion of shafts with a diameter between 18.987mm and 19.000 mm? The proportion of shafts with diameter between 18.987mm and 19.000 mm is enter your response here.A production line operates with a mean filling weight of 16 ounces per container. Overfilling or underfilling presents a serious problem and when detected requires the operator to shut down the production line to readjust the filling mechanism. From past data, a population standard deviation σ =0.8 ounces is assumed. A quality control inspector selects a sample of 29 items every hour and at the time makes the decision of whether to shut down the line for readjustment. The level of significance is α=0.05 If a sample mean of = 15.42 ounces were found, what is your calculated test statistic? (keep two decimal places of your answer)The breakdown voltages of the cables manufactured by a company have a mean of 1780 Nw and a standard deviation of 107 Nw. It is desired to check whether a new manufacturing process modifies said average breaking stress. To do this, a 78 cable sample is taken and its mean breakdown voltage is found to be 1800 Nw. The question is: Can it be said that the new manufacturing process has modified the mean breakdown stress to the 7 % significance level ? To do this, we follow the following steps: Choose the null hypothesis: a. H1 : μ ≠ 1780 b. H0: μ = 1780 Indicates Zα/2 for the significance level of 7%: Indicate the lower end of the acceptance interval (we refer to the N (0,1) distribution): Indicates the upper end of the acceptance interval (we refer to the N (0,1) distribution): Indicates the standardized value of the test statistic, z: Please indicate which of the following statements is true: a. Z ∉ (-zα/2 , zα/2) b. Z ∈ (- zα/2 , zα/2) And therefore, it indicates what to…
- Prior to the institution of a new safety program, the average number of on-the-job accidents per day at a factory was 4.5. To determine if the safety program has been effective in reducing the average number of accidents per day, a random sample of 30 days is taken after the institution of the new safety program and the number ofaccidents per day is recorded. The sample mean and standard deviation were computedas follows:Sample mean = 3.7, standard deviation = 1.3a. Is there sufficient evidence to conclude that the average number of on-the-jobaccidents per day at the factory has decreased since the institution of the safetyprogram?b. What is the practical interpretation of the test statistic computed in part a?d onlyBenzene is a toxic chemical used in the manufacturing of medicinal chemicals, dyes, artificial leather, and linoleum. A manufacturer claims that its exit water meets the federal regulation with a mean of less than 7980 ppm of benzene. To assess the benzene content of the exit water, 10 independent water samples were collected and found to have an average of 7912 ppm of benzene. Assume a known standard deviation of 90 ppm and use a significance level of 0.01.(a) Test the manufacturer’s claim. Use the P-value approach. Round your answer to 5 decimal places (e.g. 98.76543).(b) What is the β-value if the true mean is 7915? Round your answer to 3 decimal places (e.g. 98.765).(c) What sample size would be necessary to detect a true mean of 7915 with a probability of at least 0.90? Round your answer up the nearest whole number, answer is exact.(d) Find a 99% one-sided upper confidence bound on the true mean. Round your answer to 2 decimal places (e.g. 98.76).
- The mean consumption of water per household in a city was 1244 cubic feet per month. Due to a water shortage because of a drought, the city council campaigned for water use conservation by households. A few months after the campaign was started, the mean consumption of water for a sample of 96 households was found to be 1164 cubic feet per month. The population standard deviation is given to be 257 cubic feet. a. Find the p-value for the hypothesis test that the mean consumption of water per household has decreased due to the campaign by the city council. Would you reject the null hypothesis at a = 0.025? Round your answer to four decimal places. p-value = We i b. Make the test of part a using the critical-value approach and a = 0.025. Zobserved Round your answer for z to two decimal places. We Ho. i Ho. We conclude that the mean consumption of water per household has due to the campaign by the city council.8. 140 migrating pigeons were caught by a biologist for data collection. The mass of these pigeons is normally distributed with mean 0.9 kg and standard deviation of deviation 0.15 kg. a) Determine the percentile rank of a pigeon weighing 1kg. b) What proportions of pigeons have weight greater than 1.1 kg or less than 0.7 Kg 31A factory that manufactures screws is performing a quality control experiment. Each object should have a length of no more than 13 centimeters. The factory believes that the length of the screws exceeds this value and measures the length of 70 screws. The sample mean screw length was 13.01 centimeters. The population standard deviation is known to be σ=0.15 centimeters. What is the null hypothesis? What is the alternative hypothesis?
- Based on a recent study, the pH level of the arterial cord (one vessel in the umbilical cord) is normally distributed with mean 7.27and standard deviation of 0.11. Find the percentage of preterm infants who have the following arterial cord pH levels. a. pH levels between 7.00 and 7.50. b. pH levels over 7.35. a. The percentage of arterial cord pH levels that are between 7.00and 7.50 is __________%. (Round to two decimal places as needed.) b. The percentage of arterial cord pH levels that are over 7.35 is _______%. (Round to two decimal places as needed.)Three industrial engineers were assigned to monitor a certain process using X-control chart with n=9, and K=2. The in-control process mean and standard deviation are 14 and 6, respectively. The probability of having one point below the LCL equals 0.001350. Help in answering the following questions: A- Estimate the ARL. B- Estimate the ATS. C- What is the amount of shift per unit of standard deviation?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.?