b. An experiment wishes to investigate the effect of three variables- pressure, temperature, and the type of catalyst on the yield in a refining process. if the experimenter intends to use three setting each for temperature and pressure and two types of catalyst. How many experimental runs will have to be conducted?
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- 2h. How long it takes paint to dry can have an impact on the production capacity of a business. An auto body & paint business invested in a paint-drying robot to speed up its process. An interesting question is, "Do all paint-drying robots have the same drying time?" To test this, suppose we sample five drying times for each of different brands of paint-drying robots. The time in minutes until the paint was dry enough for a second coat to be applied was recorded. Suppose the following data were obtained. Robot 1 Robot 2 Robot 3 Robot 4 127 145 134 149 137 133 144 141 135 143 137 136 125 146 137 141 141 128 128 153 Find the value of the test statistic. (Round your answer to two decimal places.) Find the p-value. (Round your answer to four decimal places.) p-value =A certain reaction was run several times using each of two catalysts, A and B. The catalysts were supposed to control the yield of an undesirable side product. Results, in units of percentage yield, for 24 runs of catalyst A and 20 runs of catalyst B are as follows: Catalyst A 4.4 3.4 2.6 3.8 4.9 4.6 5.2 4.7 4.1 2.6 6.7 4.1 3.6 2.9 2.6 4.0 4.3 3.9 4.8 4.5 4.4 3.1 5.7 4.5 Catalyst B 3.4 1.1 2.9 5.5 6.4 5.0 5.8 2.5 3.7 3.8 3.1 1.6 3.5 5.9 6.7 5.2 6.3 2.6 4.3 3.8 Construct a histogram for the yields of each catalyst. Construct comparative boxplots for the yields of the two catalysts. a. b. Using the boxplots, what differences can be seen between the results of the yields of the two catalysts? C.7. In the manufacturing of a chemical adhesive, 3% of all batches have raw materials from two different lots. This occurs when holding tanks are replenished and the remaining portion of a lot is insufficient to fill the tanks. Only 5% of batches with material from a single lot require reprocessing. However, the viscosity of batches consisting of two or more lots of material is more difficult to control, and 40% of such batches require additional processing to achieve the required viscosity. Let A denote the event that a batch is formed from two different lots, and let B denote the event that a lot requires additional processing. Determine the following probabilities: а. Р(А) b. P(A') c. P(B|A) d. P(B|A') e. P(ANB) f. P(ANB') д. P(B)
- 14) Penicillin is produced by the Penicillin fungus, which is grown in a broth whose sugar be carefully controlled. Several samples of broth were taken on three successive days, and the amount of dissolved sugars, in milligrams per milliliter, was measured on each sample. The results were as follows.A certain reaction was run several times using each of the two catalysts, A and B. The catalysts were supposed to control the yield of an undesirable side product. Results, in units of percentage yield, for 24 runs of catalyst A and 20 runs of catalyst B are as follows: Catalyst A Catalyst B 4.4 3.4 2.6 3.8 3.4 1.1 2.9 5.5 4.9 4.6 5.2 4.7 6.4 5.0 5.8 2.5 4.1 2.6 6.7 4.1 3.7 3.8 3.1 1.6 3.6 2.9 2.6 4.0 3.5 5.9 6.7 5.2 4.3 3.9 4.8 4.5 6.3 2.6 4.3 3.8 4.4 3.1 5.7 4.5 Construct comparative boxplots for the yields of the two catalysts and explain the role the whisker plays in data analysis. b. Interpret what the box plot for catalyst B, communicate in real life? a.For each of the questions 1-4, answer the following (a-h are steps in a Hypothesis Test, see page 376 of your ebook). For steps f and g do both the p-value method and the critical value method: a) Claim in English: b) Claim in Symbolic Form: c) Null and Alternate Hypothesis: d) Significance Level: e) Test Statistic: f) Find Values: g) Make a Decision: h) Restate the Decision in Nontechnical Terms: i) If this is a statistically significant result, is it also a practically significant result?
- 1. Life-saving drug: Penicillin is produced by the Penicillium fungus, which is grown in a broth whose sugar content must be carefully controlled. Several samples of broth were taken on three successive days, and the amount of dissolved sugars, in milligrams per milliliter, was measured on each sample. The results were as follows. Day 1: 4.8 5.1 5.1 4.8 5.2 4.9 5.0 4.9 5.0 4.8 4.8 5.1 5.0 Day 2: 5.4 5.0 5.0 5.1 5.2 5.1 5.3 5.2 5.2 5.1 5.4 5.2 5.4 Day 3: 5.7 5.1 5.3 5.5 5.3 5.5 5.1 5.6 5.3 5.2 5.5 5.3 5.4 a. Construct an ANOVA table. b. Can you conclude that the mean sugar concentration differs among the three days? Use the α = 0.05 level of significance.Two different analytical methods were used to determine residual chlorine in sewage effluents. Both methods were used on the same samples, but each sample came from various locations with differing amounts of contact time with the effluent. Two methods were used to determine the concentration of Cl in mg/L, and the results are shown in the following table: Sample Method A Method B 1 0.39 0.36 2 0.84 1.35 3 1.76 2.56 4 3.35 3.92 5 4.69 5.35 6 7.70 8.33 7 10.52 10.70 8 10.92 10.91 a) What type of t-test should be used to compare the two methods and why? b) Do the two methods give different results? State and test the appropriate hypotheses. c) Does the conclusion depend on whether the 90%, 95%, or 99% confidence levels are used?4. Two different analytical methods were used to determine residual chlorine in sewage effluents. Both methods were used on the same samples, but each came from various locations, with differing amounts of contact time with the effluent. The concentration of Cl in mg/L was determined by the two methods, and the following results were obtained:Method A: 0.39, 0.84, 1.76, 3.35, 4.69, 7.70, 10.52, 10.92Method B: 0.36, 1.35, 2.56, 3.92, 5.35, 8.33, 10.70, 10.91What type of t test should be used to compare the two methods and why? (b) Do the two methods give different results? (c) Does the conclusion depend on whether the 90%, 95% or 99% confidence levels are used?
- You want to determine the effect of soap on bacterial colonies. In order to make sure that the environmentdoes not affect your experiment, you divide 13 different petri dishes in half - one side is exposed to soap, theother is a control.You measure the number of colonies that grow in each petri dish and come up with the following results:petri dish 1 2 3 4 5 6 7 8 9 10 11 12 13soap 10 5 7 10 19 11 13 17 19 8 11 10 16control 20 17 11 17 26 18 21 25 24 17 17 17 21Perform a complete hypothesis test to see if there is a difference in bacterial colonies between the soapand control dishes.Again - notice that you are given no advice. You need to figure this out on your own, althoughthis one should be a bit easier than (4). Feel free to use R to solve this problem, just make sureyou don't just hand in a printout.Two different analytical methods were used to determine residual chlorine in sewage effluents. Both methods were used on the same samples, but each sample came from various locations with differing amounts of contact time with the effluent. Two methods were used to determine the concentration of Cl in mg/L, and the results are shown in the following table: Sample Method A Method B 0.36 1.35 2.56 3.92 5.35 1 0.39 2 0.84 3 1.76 3.35 4.69 4 8.33 10.70 7.70 7 10.52 8 10.92 10.91 a. What type of t test should be used to compare the two methods and why? b. Do the two methods give different results? State and test the appropriate hypotheses. Does the conclusion depend on whether the 90%, 95%, or 99% confidence levels с. are used?4. A gravity concentration plant is processing 10,000 MT/D of gold ore. In order to attain a reasonable 90% overall recovery for the plant, what feed assay should the plant maintain to have at least a ratio of concentration of 1000. The grade of concentrate it produces is 1000 gm of Au / MT. 64Also, if the current price of gold is $400 per ounce, determine the total money lost by the plant per day due to tailings