The following data were obtained from a company that manufactures special plastic containers that are to hold a specified volume of hazardous material. On each of the three 8-hour shifts workers are able to make 500 of the containers. Some containers do not meet specifications as required by the company's customer because they are too small; others, because they are too large.

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?

5. The local aquaritum is repurposing a large occan exchibit into a prescutation of estuaries. The tank bolds 10.000 aallons of water. The current ocean exhibit contains 2800 pounds of salt. The desired concentration for the new exhibit is 0.1 pounls per galkon. Fresh water will be adled to the tank at a coustant rate of 10 gallous per minutle. The solution in the tank immediately mixes thoronghly and drains at a rate of 10 gallons per mimte. a. Wrile lhe diflerenulial equatini ansl initial conuditions represenilmng ilhe anenail of sall, S, in the lank. Dis nol solve dr h. Salve the differential equation you kumd in part a. Your linal equation should be an equation for S in tenns of * (in minutes).

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The specification for the pull strength of a wire that connects an integrated circuit to its frame is 10 g or more. Units made with aluminum wire have a defect rate of 10%. A redesigned manufacturing process, involving the use of gold wire, is being investigated. The goal is to reduce the rate of defects to 5% or less. Out of the first 100 units manufactured with gold wire, only 4 are defective. True or false: a) Since only 4% of the 100 units were defective, we can conclude that the goal has been reached. b) Although the sample percentage is under 5%, this may represent sampling variation, so the goal may not yet be reached. c) There is no use in testing the new process, because no matter what the result is, it could just be due to sampling variation. d) If we sample a large enough number of units, and if the percentage of defective units is far enough below 5%, then it is reasonable to conclude that the goal has been reached.

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.

9. You need to pipette 30 mL in lab as accurately as possible, but you only have a Class B 10- mL pipette and a Class A 5-mL volumetric pipette. Is it more accurate to use the Class B pipette three times or the Class A pipette six times? The Class B pipette has a tolerance of 0.04 mL and the Class A pipette has a tolerance of 0.01 mL.

A study was conducted by the Department of Biological Sciences at Virginia Tech to determine if there is a significant difference in the density of organisms at two different stations located on Cedar Run, a secondary stream in the Roanoke River drainage basin. Sewage from a sewage treatment plant and overflow from the Federal Mogul Corporation settling pond enter the stream near its headwaters. The accompanying data give the density measurements, in number of organisms per square meter, at the two collecting stations. Can it be concluded, at the 0.05 level of significance, that the average densities at the two stations are equal? Assume that the observations come from normal populations with different variances. Click the icon to view the data on organisms per square meter. Let sample 1 be the station 1 data and let sample 2 be the station 2 data. State the null and alternative hypotheses. Hoi Hy-H2 = 0 H₁ H1 H2 0 (Type integers or decimals. Do not round.) Find the test statistic. The…

PT. X is an industry engaged in concrete steel with various diameter sizes. The product that is mostly produced is concrete iron with a diameter of 12 mm because it suits the needs of consumers and the current pandemic conditions. During the period from January to December 2019, PT. X is capable of producing as many as 6800 tonnes of units. From the results produced, there is a product defect of 70.4 with the type of product damage, namely overfill (wing), overlap (excessive shape), underfill (kempong) and scratch (beret). In that period, defects were found above the tolerance limit of 2%, namely at week 5 and week 12 of 2.42% and 2.21%. During the production process PT.X has a 2% probability of producing defective products. If you check is 065, then determine:a. P(X=0)b. P(X=1)c. P(X=2)d. P(X≤2)e. P(X≥3)

2. A valve manufacturer produces a butterfly valve composed of twosemicircular plates on a common spindle that is used to permit flow inone direction only. The semicircular plates are supplied by a vendor withspecifications that the plates be 2.37 millimeters thick and have a tensilestrength of five pounds per millimeter. A random sample of 20 suchplates is taken. Electronic calipers are used to measure the thickness ofeach plate. A universal testing machine was used to test the tensilestrength. The sample data are found Below.  a. Determine, with 95% confidence, if mean tensile strength is less than five pounds permillimeter. Use the critical value approach.b. Are more than half of plates thicker than 2.37? Use the p-value approach with 95%confidence.  Thickness Strength 2.4066 4.9175 2.1328 4.8067 2.5937 5.1246 2.1933 4.7555 2.4579 4.7233 2.0665 4.3934 2.1994 4.4609 2.4575 4.7377 2.6724 4.3407 2.2738 4.9487 2.5392 4.4265 2.7956 4.3583 2.1228 4.5608…