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- Radon is a gas emitted from the ground that can collect in houses in buildings. At certain levels it can cause lung cancer. Radon concentrations are measured in picocuries per liter (pCi/L). A radon level of 4 pCi/L is considered “acceptable” Radon levels in a house vary from week to week. In one house, a sample of 6 weeks had the following readings for radon level (in pCi/L): 1.9 2.8 3.9 3.9 4.2 5.7 Find the variance and standard deviation (definitional formula). Show your work using a table.Fifty male subjects drank a measured amount x (in ounces) of a medication and the concentration y (in percent) in their blood of the active ingredient was measured 30 minutes later. The sample data are summarized by the following information: n = 50 Ex = 112.5 Ex? = 356.25 %3D Ey = 4.83 Ey = 0.667 Exy = 15.255 0 < x < 4.5 Or= 0.875 Or= 0.709 Or= -0.846 Or=0.460 Or= 0.965In a study of processes used to remove impurities from cellulose goods, the following data resulted from a 24 experiment involving the desizing process. The four factors were enzyme concentration (A), PH (8), temperature (C), and time (0). Starch % by Weight Enzyme Temp. Time 1st Treatment (g/L) PH (1) 0.50 6.0 (°C) (hr) 60.0 2nd Repl. Repl. 6 9.72 13.50 а 0.75 6.0 60.0 6 9.80 14.04 b 0.50 7.0 60.0 6 10.13 11.27 ab 0.75 7.0 60.0 6 11.84 11.30 c 0.50 6.0 70.0 6 12.70 11.37 ac 0.75 6.0 70.0 6 11.96 12.05 bc 0.50 7.0 70.0 6 11.38 9.92 abc 0.75 7.0 70.0 6 11.80 11.14 d 0.50 6.0 60.0 8 13.15 13.00 ad 0.75 6.0 60.0 8 10.60 12.37 bd 0.50 7.0 60.0 8 10.37 12.00 abd 0.75 7.0 60.0 8 11.30 11.64 cd 0.50 6.0 70.0 8 13.05 14.55 acd 0.75 6.0 70.0 8 11.17 15.00 bcd 0.50 7.0 70.0 abcd 0.75 7.0 70.0 8 8 12.70 14.15 13.20 16.12 (a) Use Yates's algorithm to obtain sums of squares and the ANOVA table. (Round your answers to two decimal places.)
- A new purification unit is installed in a chemical process. Before its installation, a random sample yielded the following data about the percentage of impurity: x1 = 9.85 , S12 = 81.73 , and n1 = 8 . After installation, a random sample resulted in x2 = 8.08 , S2 = 78.46 , and n2 = 10 .The following data are from an experiment on carnations. The explanatory variable is the amount of inorganic bromine (micrograms per milliliter) in a plot of standard size. The response variable is the average number of flowers per carnation plant for the 30 plants grown in the plot. Find the change in number of flowers per plant given an increase in 1 µg per mL of inorganic bromine. Amount of bromine Average no. of flowers Select one: O a. -0.216 O b. 0.216 O c. O d. -3.81 4.04 3 3.2 4 2.9 6 3.7 7 2.2 8 1.8 10 2.3 12 1.7 15 16 0.8 0.3A researcher wanted to know if there was a relationship between stress and frustration. Theresearcher recruited n = 5 participants and asked them to solve a difficult puzzle in a short timeperiod. She then asked each participant to rate how stressful the task was and how frustratedthey were to solve the puzzle on a scale of 1 to 5. The data are below: Stress (X) Frustration (Y) 2 1 2 2 3 4 3 4 3 5 Calculate the sum of products
- In a study of crop losses due to air pollution, plots of Blue Lake snap beans were grown in open-top field chambers, which were fumigated with various concentrations of sulfur dioxide. After a month of fumigation, the plants were harvested, and the total yield of bean pods were recorded for each chamber. Suppose X = sulfur dioxide concentration (ppm) and Y = yield (kg). Here is the information about the data. n = 17, xbar (sample mean of X) = 0.12, ybar (sample mean of Y) =1.117, sX = 0.11724, sY = 0.31175, r = -0.8506, SS(resid) = 0.2955 residual standard deviation (se) = 0.14 slope of the least-squares regression line: -2.26 Using the given information, what is the standard error of the slope (SEb1)? what’s the value of the test statistic (ts)?A pet food company is concerned that their pet food must have a certain % of the mineral 2Ine II the food. Too little and dogs get very sick. If the machinery is working correctly, the average zinc is µu = .375 gram/lb of food. They sample 25 bags of food and find: x = .359 grams o = .05 grams The firm wants to know if their pet food is healthy. They decide on a 95% level of significance. Do the Z test. They ask you to perform the analysis. a) State the null and alternative hypotheses. Ho: На: b) Draw a picture/graph of what you are trying to find. c) Find the critical value you will use. d) Compute the test statistic (from the data) e) What do you conclude? Why?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 44 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 = 8.00 ml/kg for the distribution of blood plasma.
- The effectiveness of a new bug repellent is tested on 1616 subjects for a 10 hour period. (Assume normally distributed population.) Based on the number and location of the bug bites, the percentage of surface area exposed protected from bites was calculated for each of the subjects. The results were as follows: ?⎯⎯⎯=92x¯=92, ?=13 s=13 The new repellent is considered effective if it provides a percent repellency of at least 9090. Using ?=0.05α=0.05, construct a hypothesis test with null hypothesis ?≤90μ≤90 and alternative hypothesis ?>90μ>90 to determine whether the mean repellency of the new bug repellent is greater than 9090 by computing the following: (a) the degree of freedom (b) the test statistic The final conclusion is A. There is not sufficient evidence to reject the null hypothesis that ?≤90μ≤90. Our results do not provide enough evidence that the new bug repellent is effective. B. We can reject the null hypothesis that ?≤90μ≤90. Our results indicate that…On the production line the company finds that 85.6% of products are made correctly. You are responsible for quality control and take batches of 30 products from the line and test them. Let X represent the number of products out of 30 that are made correctly. What value(s) of X would cause you to shut down production?The quality control engineer at Palmer Industries is interested in estimating the tensile strength of steel wire based on its outside diameter and the amount of molybdenum in the steel. As an experiment, she selected 25 pieces of wire, measured the outside diameters, and determined the molybdenum content. Then she measured the tensile strength of each piece. The results of the first four are recorded in the table. Tensile Strength Outside Diameter Amount of Molybdenum Place (PSI ) Y (mm) X1 (Units) X2 A 11 0.3 6 B 9 0.2 5 C 16 0.4 8 D 12 0.3 7 Using a statistical software package, the QC engineer determined the multiple regression equation to be Y’=-0.5+20X1+1X2. a) Based on the equation, what is the estimated tensile strength of a steel wire having an outside diameter of .35 mm and 6.4 units of molybdenum? b) Interpret the value of b1 in the equation.
