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- 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.2. Ceramic items are "baked" in a gas-fired tubular-shaped oven is lots of 100 units. The items are lined up in a single row on a special high-temperature pallet, slid into the oven, the oven closed, and the temperature increased manually according to time-temperature scale. After cooling, a sample of five units is drawn from a lot and strength-tested by breaking them in a special testing device. To be effective in use, breaking strength must exceed 5 psi. If any item breaks at less than 5 psi, the lot from which it came is scrapped. About 10% of the lots have been scrapped in recent times. a. A decision is made to run a process capability study. Data on the next 20 lots are tested using the same procedure, and a sample sized of 5, and X-bar and R charts are drawn. At this point, IX = 112.00 psi and ER = 23.26 psi. Calculate control limits for X and R for this process and estimate o b. Assuming a normal distribution of product, what proportion would you estimate does not meet…5. Seventy percent of clay pots are produced by Machine 1 and 30% by Machine 2. Among all pots produced by Machine 1, 4% are defective, and of those produced by Machine 2, 8% are defective. a) What percentage of the total produced are defective? (0.70)(0.04) + (0.30)(0.08) = 0.052 or 5.2% b) If a pot is found to be defective, what is the probability that it was produced by Machine 2? Explain your answer. (0.30)(0.08) 0.052 = 0.4615 or 46.2%
- 2. Ceramic items are "baked" in a gas-fired tubular-shaped oven is lots of 100 units. The items are lined up in a single row on a special high-temperature pallet, slid into the oven, the oven closed, and the temperature increased manually according to time-temperature scale. After cooling, a sample of five units is drawn from a lot and strength-tested by breaking them in a special testing device. To be effective in use, breaking strength must exceed 5 psi. If any item breaks at less than 5 psi, the lot from which it came is scrapped. About 10% of the lots have been scrapped in recent times. c. Calculate the pertinent Process Capability Indexes for this process and interpret their meaning relative to your answer to part (b) d. Assuming R chart shows good control, where should the process be centered to ensure that no more than 0.1% of the items do not meet specification (assume a normal distribution)? Calculate the same Process Capability Indexes at this target mean setting.6) An aircraft firm is considering three different alloys for use in the wing construction of a new airplane. Each alloy can be produced in four different thicknesses (1 = thinnest, 4 = thickest). Two test samples are constructed for each combination of alloy type and thickness, then each of the 24 test samples is subjected to a laboratory device the severely flexes it until failure occurs. For each test sample the number of flexes before failure is recorded, with the data shown below. a) Use JMP to fit a two-way ANOVA to the data. Using a = 0.05 draw conclusions for the ANOVA. Make sure you state your conclusion in the context of the problem. b) Does there appear to be a need to include the alloy type / thickness interaction term? c) Use JMP to fit a two-way ANOVA with interaction to the data. Using a = 0.05 draw conclusions for the ANOVA. Make sure you state your conclusion in the context of the problem. Alloy Thickness Flexes Alloy A Thickness 1 804 Alloy A Thickness…A sporting equipment company makes three different types of balls: soccer balls, basketballs, and cork balls. Respectively, their production times are 3, 4, and 3.5 hours for each. The quality of the balls is tested using any one of the two procedures, P1 and P2. Once the product is tested, it is sent to packaging. Procedure P1 requires 1.5, 2, and 3.5 hours for each soccer ball, basketball, and cork ball respectively. Procedure P2 requires 3, 1.6, and 2 hours for each type of ball respectively. The total available production time for the next month is 300 hours. Available times for procedure P1 is 175 hours, and procedure P2 is 195 hours. Unit profit for each soccer ball, basketball, and cork ball is $9, $ 6, $7 respectively. What is the maximum profit?
- 2. Ceramic items are “baked” in a gas-fired tubular-shaped oven is lots of 100 units. The items are linedup in a single row on a special high-temperature pallet, slid into the oven, the oven closed, and thetemperature increased manually according to time-temperature scale. After cooling, a sample of fiveunits is drawn from a lot and strength-tested by breaking them in a special testing device. To beeffective in use, breaking strength must exceed 5 psi. If any item breaks at less than 5 psi, the lot fromwhich it came is scrapped. About 10% of the lots have been scrapped in recent times.a. A decision is made to run a process capability study. Data on the next 20 lots are tested using thesame procedure, and a sample sized of 5, and X-bar and R charts are drawn. At this point, ΣX = 112.00psi and ΣR = 23.26 psi. Calculate control limits for X and R for this process and estimate σb. Assuming a normal distribution of product, what proportion would you estimate does not meetspecifications?c.…6. A geologist collected 20 different ore samples, all of the same weight, and randomly divided them into two groups. The titanium contents of the samples, found using two different methods are listed below: Method 1 Method 2 .011 .013 .013 .015 .014 .011 .016 .013 .012 .015 013 .010 .013 .011 .012 .012 .017 .013 .014 .015 Use an appropriate test statistic to test for significant difference in the average titanium contents using a = 0.05.1. Soil samples were collected at two areas surrounding an abandoned mine and analyzed for lead. At each area several samples were taken. The soil was extracted with acid, and the extract was analyzed using flame atomic absorption spectrometry. In Area A, Pb concentrations were 1.2, 1.0, 0.9, 1.4 mg/kg. In Area B, Pb concentrations were 0.7, 1.0, 0.5, 0.6, 0.4 mg/kg. Are these two areas significantly different from each other with Pb concentrations at 90% confidence level?
- 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 =2. In a science fair project, Emily conducted an experiment in which she tested professional touch therapists to see if they could sense her energy field. She flipped a coin to select either her right hand or left hand, and then she asked the therapists to identify the selected hand by placing their hand just under Emily's hand without seeing it and without touching it. Among 300 trials, the touch therapists were correct 135 times. Complete parts (a) through (d) a. Given that Emily used a coin toss to select either her right hand or her left hand, what proportion of correct responses would be expected if the touch therapists made random guesses? b. Using Emily's sample results, what is the best point estimate of the therapist's success rate? c. Using Emily's sample results, construct a 99% confidence interval estimate of the proportion of correct responses made by touch therapists. d. What do this result suggest about the ability of touch therapists to select the correct hand by seeing…3. Two analysts were given a standard reference material (SRM) and were asked to determine its copper concentration (in mg/kg) using the EPA standard method. Each analyst was given sufficient time so they could produce as many accurate results as possible. Their results (mg/kg) were as follows: Analyst A 45.2, 47.3, 51.2, 50.4, 52.2, 48.7 (Standard error s = 2.62) Analyst B 49.4, 50.3, 51.6, 52.1, 50.9 (Standard error s = 1.06) (a) For Analyst A, is 52.2 mg/kg a possible outlier? (b) Calculate the RSD for each student; which analyst is more precise? (c) If the known concentration of copper in SRM is 49.5 mg/kg, which analyst is more accurate (without considering the deletion of outliers if any)?