Suppose that you wish to estimate the difference between mean pH measurements of rainfalls in two different locations, one in relatively unpolluted area and the other in an area subject to heavy air pollution. You want to be 95 % confident that the margin of error for the difference between mean pH of rainfalls in relatively unpolluted area and mean pH of rainfalls in an area subject to heavy air pollution will not exceed 0.1 pH. How many rainfalls (pH measurements) must be included in each sample? Assume that the variance of pH measurements in a relatively unpolluted area is equal to 2 o = 20, and the variance of pH measurements in an area subject to heavy pollution is equal to 2 ₁ = 0.25, and samples will be of equal size (n₁ = n₂ = n). It is supposed that values of pH in rainfalls are normally distributed in polluted and unpolluted areas. The number of rainfalls (pH measurements) that must be included in each sample is

The population mean will always be the same as the mean of all possible X¯ that can be computed from samples of size 21.

Total plasma volume is important in determining the required plasma component in blood replacement therapy for a person undergoing surgery. Plasma volume is influenced 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 ? = 7.80 ml/kg for the distribution of blood plasma. (d) Find the sample size necessary for a 99% confidence level with maximal margin of error E = 2.00 for the mean plasma volume in male firefighters. (Round up to the nearest whole number.) male firefighters

Hemoglobin is a protein in red blood cells that transports oxygen from the lungs to the body's tissues. People with less than 12 grams of hemoglobin per deciliter of blood (g/dl) are anemic. A public health official in Oklahoma suspects that the mean hemoglobin of children in his city is different than 12. (a) µ represents the population mean of children in Oklahoma. (b) State the hypotheses (Ho & Ha) for a test to verify the public health official's belief. (c) State what the parameter u in your hypotheses is.

Suppose u, and u, are true mean stopping distances at 50 mph for cars of a certain type equipped with two different types of braking systems. The data follows: m = 5, x = 115.1, s, = 5.05, n = 5, y = 129.2, and s, = 5.36. Calculate a 95% CI for the difference between true average stopping distances for cars equipped with system 1 and cars equipped with system 2. (Round your answers to two decimal places.) n USE SALT Does the interval suggest that precise information about the value of this difference is available? O Because the interval is so narrow, it appears that precise information is available. o Because the interval is so wide, it appears that precise information is not available. o Because the interval is so narrow, it appears that precise information is not available. Because the interval is so wide, it appears that precise information is available. You may need to use the appropriate table in the Appendix of Tables to answer this question.

Unfortunately, arsenic occurs naturally in some ground water.† A mean arsenic level of μ = 8.3 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 41 tests gave a sample mean of x = 7.3 ppb arsenic, with s = 2.4 ppb. Does this information indicate that the mean level of arsenic in this well is less than 8.3 ppb? Use ? = 0.01.   (a) What is the level of significance?   State the null hypotheses  H0  and the alternate hypothesis  H1 . H0 : μ  ---Select--- < ≥ ≤ = > ≠   H1 : μ  ---Select--- < >  ≤ ≥ = ≠  (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 σ is known.The Student's t, since the sample size is large and σ is known.     The standard normal, since the sample size is large and σ is unknown. The Student's t, since the…

To check the effect of hot temperatures on the elasticity of two brands of rubber bands, one box of Brand A and one box of Brand B rubber bands are tested. Ten bands from the Brand A box are placed in a warm car in the sun for two hours and ten bands from the Brand B box are kept at room temperature. The amount of stretch before the breakage is measured on each rubber band, and the mean for the hot bands is compared to the mean for the others. Is this a good experimental design? No, because No, because temperature is confounded No, because No, because the means are more than two more not proper Yes brands should temperatures should be used. statistics for be used. with brand. comparison.

Trace 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.

pan's high population density has resulted in a multitude of resource-usage problems. One especially serious difficulty concerns waste removal. An article reported the development of a new compression machine for processing sewage sludge. An important part of the investigation involved relating the moisture content of compressed pellets (y, in %) to the machine's filtration rate (x, in kg-DS/m/hr). The following data was read from a graph in the article. x 125.8 98.1 201.4 147.3 145.9 124.7 112.2 120.2 161.2 178.9 159.5 145.8 75.1 151.5 144.2 125.0 198.8 133.9 y 77.9 76.8 81.5 79.8 78.2 78.3 77.5 77.0 80.1 80.2 79.9 79.0 76.9 78.2 79.5 78.1 81.5 71.0 (a) Determine the slope and intercept of the estimated regression line. (Round your answers to 5 decimal places, if needed.)slope: intercept: (b) Does there appear to be a useful linear relationship? Carry out a test using the ANOVA approach and a significance level of 0.05. State the appropriate null and alternative hypotheses.…

A researcher is interested in testing the relationship between smoking and BMI (kg/m2) in adults aged 30-45. In order to test this association, the researcher divides smoking into currently more than a pack a day, currently less than a pack a day, and never smokers. The following table represents the BMIs for each participant enrolled by their respective smoking category. Current Smoker (≥1pack/day) Current Smoker (<1 pack/day Never Smoked 26.7 29.4 22.1 29.4 28.6 30.4 24.3 27.4 21.3 28.4 23.2 26.4 21.6 20.1 19.7 27.4 20.6 19.8 26.8 19.7 21.6 36.4 19.6 22.3 31.5   21.6 24.3   27.4 21.5     *Continue as though all assumptions for ANOVA are met. A) Calculate the MSW and MSB for the data represented above. B) Carry out a formal test for a one-way analysis of variance among the groups and interpret your results.