In the manufacturing process of a pharmaceutical product, repeated measurements of the concentration of the active ingredient follow a Normal distribution with mean u equal to the true product concentration, and with standard deviation = 0.008 g/l. How many measurements would be needed to estimate the true concentration within ±0.001 g/l with 95% confidence? Give your answer rounded up to the nearest whole number. n=
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- One company's bottles of grapefruit juice are filled by a machine that is set to dispense an average of 180 milliliters (ml) of liquid. A quality-control inspector must check that the machine is working properly. The inspector takes a random sample of 40 bottles and measures the volume of liquid in each bottle. We want to test Hg: μ = 180 Ha: 180 where μ = the true mean volume of liquid dispensed by the machine. The mean amount of liquid in the bottles is 179.6 ml and the standard deviation is 1.3 ml. A significance test yields a P-value of 0.0589. Interpret the P-value. Assuming the true mean volume of liquid dispensed by the machine is 180 ml, there is a 0.0589 probability of getting a sample mean of 179.6 just by chance in a random sample of 40 bottles filled by the machine. Assuming the true mean volume of liquid dispensed by the machine is 180 ml, there is a 0.0589 probability of getting a sample mean at least as far from 180 as 179.6 (in either direction) just by chance in a…Unfortunately, arsenic occurs naturally in some ground water.t A mean arsenic level of u = 8.0 parts per billion (ppb) is considered safe for agricultural use. A well in Texas is used to water cotton crops. This well is tested on a regular basis for arsenic. A random sample of 36 tests gave a sample mean of x = 7.1 ppb arsenic, with s = 2.2 ppb. Does this information indicate that the mean level of arsenic in this well is less than 8 ppb? Use a = 0.01. A USE SALT (a) What is the level of significance? State the null and alternate hypotheses. O Họ: u = 8 ppb; H,: u > 8 ppb O Ho: H 8 ppb; H,: u = 8 ppb (b) What sampling distribution will you use? Explain the rationale for your choice of sampling distribution. The standard normal, since the sample size is large and a is unknown. O The Student's t, since the sample size is large and a is known. O The standard normal, since the sample size is large and a is known. The Student's t, since the sample size is large and a is unknown. What is the…Unfortunately, arsenic occurs naturally in some ground water.t A mean arsenic level of u = 8.0 parts per billion (ppb) is considered safe for agricultural use. A well in Texas is used to water cotton crops. This well is tested on a regular basis for arsenic. A random sample of 36 tests gave a sample mean of x = 7.1 ppb arsenic, with s = 2.2 ppb. Does this information indicate that the mean level of arsenic in this well is less than 8 ppb? Use a = 0.01. A USE SALT (a) What is the level of significance? State the null and alternate hypotheses. O Ho: H= 8 ppb; H,: H > 8 ppb O Ho: H 8 ppb; H: H = 8 ppb (b) What sampling distribution will you use? Explain the rationale for your choice of sampling distribution. O The standard normal, since the sample size is large and a is unknown. O The Student's t, since the sample size is large and a is known. O The standard normal, since the sample size is large and a is known. O The Student's t, since the sample size is large and a is unknown. What is…
- Unfortunately, arsenic occurs naturally in some ground water.t A mean arsenic level of u = 8.0 parts per billion (ppb) is considered safe for agricultural use. A well in Texas is used to water cotton crops. This well is tested on a regular basis for arsenic. A random sample of 36 tests gave a sample mean of x = 6.7 ppb arsenic, with s = 3.0 ppb. Does this information indicate that the mean level of arsenic in this well is less than 8 ppb? Use a = 0.01. n USE SALT (a) What is the level of significance? State the null and alternate hypotheses. O Ho: H = 8 ppb; H,: u > 8 ppb O Ho: H = 8 ppb; H,: H + 8 ppb O Ho: H 8 ppb; H,: u = 8 ppb O Ho: H = 8 ppb; H,: µ 0.100 O 0.050 < P-value < 0.100 O 0.010 < P-value < 0.050 O 0.005 < P-value < 0.010 P-value < 0.005 Sketch the sampling distribution and show the area corresponding to the P-value. MacBook Pro escTrace metals in drinking water affect the flavor and an unusually high concentration can pose a health hazard. Ten pairs of data were taken measuring zinc concentration in bottom water and surface water. The raw data provided in table below. Does the data suggest that the true average concentration in the bottom water exceeds that of surface water? Use ?=0.01.Total plasma volume by the overall health and physical activity of an individual. Suppose that a random sample of 40 male firefighters are tested and that they have a plasma volume sample mean of x = 37.5 ml/kg (milliliters plasma per kilogram body weight). Assume that o = 7.10 ml/kg for the distribution of blood plasma. is important in determining the required plasma component in blood replacement therapy for a person undergoing surgery. Plasma volume is influenced When finding an 99% confidence interval, what is the critical value for confidence level? (Give your answer to two decimal places.) z. = (a) Find a 99% confidence interval for the population mean blood plasma volume in male firefighters. What is the margin of error? (Round your answers to two decimal places.) lower limit upper limit margin of error (b) What conditions are necessary for your calculations? (Select all that apply.) n is large the distribution of volumes is normal o is unknown the distribution of volumes is…
- The mean value of the weight of product X is normally distributed with average (0.297 kg) and Standard deviation (0.024 kg). Find the percentage of product that their weights are below 0.274 kg?Suppose the lengths of human pregnancies are normally distributed with u = 266 days and 0 = 16 days. The figure to the right represents the normal curve with u = 266 days and 0 = 16 days. The area to the left of X = 245 is 0.0947. Provide two interpretations of this area.An insulating material process produces sheets whose thickness is lognormally distributed with mean, μ = 8.5 inches and standard deviation, σ = 2.0 inches. Please calculate the thickness that 80.0 percent of the products thicknesses are thinner than or equal to.
- Overproduction of uric acid in the body can be an indication of cell breakdown. This may be an advance indication of illness such as gout, leukemia, or lymphoma.t Over a period of months, an adult male patient has taken thirteen blood tests for uric acid. The mean concentration was x = 5.28 mg/dl. The distribution of uric acid in healthy adult males can be assumed to be normal, with o = 1.91 mg/dl. (a) Find a 95% confidence interval for the population mean concentration of uric acid in this patient's blood. What is the margin of error? (Round your answers to two decimal places.) lower limit upper limit margin of error (b) What conditions are necessary for your calculations? (Select all that apply.) o is known n is large o is unknown normal distribution of uric acid uniform distribution of uric acid (c) Interpret your results in the context of this problem. We are 5% confident that the true uric acid level for this patient falls within this interval. The probability that this interval…Overproduction of uric acid in the body can be an indication of cell breakdown. This may be an advance indication of illness such as gout, leukemia, or lymphoma. Over a period of months, an adult male patient has taken 8 blood tests for uric acid. The mean concentration was x = 5.35 mg/dl. The distribution of uric acid in healthy adult males can be assumed to be normal, with σ = 1.85mg/dl.(a) Find a 95% confidence interval for the population mean concentration of uric acid in this patient's blood. What is the margin of error? (b) What conditions are necessary for your calculations? (c) interpret your results in the context of this problem. (d)Sample size find the sample size necessary for a 95% confidence level maximal margin of error E=1.10 for the mean concentration of uric acid in this patient's blood.Overproduction of uric acid in the body can be an indication of cell breakdown. This may be an advance indication of illness such as gout, leukemia, or lymphoma.t Over a period of months, an adult male patient has taken eleven blood tests for uric acid. The mean concentration was x = 5.31 mg/dl. The distribution of uric acid in healthy adult males can be assumed to be normal, with o = 1.79 mg/dl. (a) Find a 95% confidence interval for the population mean concentration of uric acid in this patient's blood. What is the margin of error? (Round your answers to two decimal places.) lower limit upper limit margin of error (b) What conditions are necessary for your calculations? (Select all that apply.) o is known o is unknown uniform distribution of uric acid On is large normal distribution of uric acid (c) Interpret your results in the context of this problem. O The probability that this interval contains the true average uric acid level for this patient is 0.95. O The probability that this…
