productlines productline VARCHAR(50) textDescription VARCHAR(4000) htmlDescription MEDIUMTEXT image MEDIUMBLOB Indexes \begin{tabular}{l} 7 employees \\ 7 employeeNumber INT(11) \\ lastName VARCHAR(50) \\ firstName VARCHAR(50) \\ extension VARCHAR(10) \\ email VARCHAR(100) \\ officeCode VARCHAR(10) \\ reportsTo INT(11) \\ jobTnte VARCHAR(50) \\ \hline \end{tabular} Indexes \( \square \) offices officeCode VARCHAR(10) \( \rho \) city VAROWR(50) phone VAROLAR(SO) addresslime 1 VAROHR(50) addresstine 2 VARCHAR(50) state VAROWAR(50) country VAROUAR(50) postalCode VARCOUR(15) territory VARCHAR(10) indexes products productCode VARCHAR(15) productName VARCHAR(70) productline VARCHAR(50) productScale VAROHAR(10) productVendor VARCHAR(50) productDescription TEXT quantityInStock SMALINT(6) buyPrice DOUBLE MSRP DOUBLE Inderes Indians creditLims DOUBLE customerNumber INT(11) checkNumber VARCHAR(SO) paymentDate DATETIME amount DOUBLE Indexes.
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The tables mentioned are `productlines`, `employees`, `offices`, `products`, and a table related to financial transactions (possibly `payments`), though its name isn't explicitly mentioned. Show moreā¦
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The company is interested in using control charts to monitor the temperature of its manufacturing process. Compute the upper and lower control limits for the R chart. (Round your answers to three decimal places.) UCL = LCL = Construct the R chart. Compute the upper and lower control limits for the xĢ chart. (Round your answers to three decimal places.) UCL = LCL = Construct the xĢ chart. What conclusions can be made about the quality of the process? The R chart indicates that the process variability is outside the R chart control limits. The xĢ chart indicates that the process mean is outside the xĢ chart control limits.
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Our number system consists of the digits $0,1,2,3,4,5,6,7,8,$ and $9 .$ The first significant digit in any number must be $1,2,3,4,5,6,7,8,$ or 9 because we do not write numbers such as 12 as 012. Although we may think that each digit appears with equal frequency so that each digit has a $\frac{1}{9}$ probability of being the first significant digit, this is not true. In $1881,$ Simon Newcomb discovered that first digits do not occur with equal frequency. This same result was discovered again in 1938 by physicist Frank Benford. After studying much data, he was able to assign probabilities of occurrence to the first digit in a number as shown. $$\begin{array}{lccccc}\text { Digit } & 1 & 2 & 3 & 4 & 5 \\\hline \text { Probability } & 0.301 & 0.176 & 0.125 & 0.097 & 0.079 \\\hline \text { Digit } & 6 & 7 & 8 & 9 & \\\hline \text { Probability } & 0.067 & 0.058 & 0.051 & 0.046 & \\\hline\end{array}$$ The probability distribution is now known as Benford's Law and plays a major role in identifying fraudulent data on tax returns and accounting books. For example, the following distribution represents the first digits in 200 allegedly fraudulent checks written to a bogus company by an employee attempting to embezzle funds from his employer. $$\begin{array}{lrrrrrrrrr}\text { First digit } & 1 & 2 & 3 & 4 & 5 & 6 & 7 & 8 & 9 \\\hline \text { Frequency } & 36 & 32 & 28 & 26 & 23 & 17 & 15 & 16 & 7 \\\hline\end{array}$$ (a) Because these data are meant to prove that someone is guilty of fraud, what would be an appropriate level of significance when performing a goodness-of-fit test? (b) Using the level of significance chosen in part (a), test whether the first digits in the allegedly fraudulent checks obey Benford's Law. (c) Based on the results of part (b), do you think that the emplovee is guilty of embezzlement?
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