WGU C723 Quantitative Analysis 100% Solved

WGU C723 Quantitative Analysis 100% Solved Based on data collected from its production processes, Crosstiles Inc. determines that the breaking strength of its most popular porcelain tile is normally distributed with a mean of 400 pounds per square inch and a standard deviation of 12.5 pounds per square inch. Based on the 68-95-99.7 Rule, about what percent of its popular porcelain tile will have breaking strengths between 375 and 425 pounds per square inch? 95% Based on data collected from its production processes, Crosstiles Inc. determines that the breaking strength of its most popular porcelain tile is normally distributed with a mean of 400 pounds per square inch and a standard deviation of 12.5 pounds per square inch. Based on the 68-95-99.7 Rule, about what percent of its popular porcelain tile will have breaking strengths greater than 412.5 pounds per square inch? 16% At a local manufacturing plant, employees must complete new machine set ups within 30 minutes. New machine set-up times can be described by a normal model with a mean of 22 minutes and a standard deviation of four minutes. What percent of new machine set ups take more than 30 minutes? 2.28% At a local manufacturing plant, employees must complete new machine set ups within 30 minutes. New machine set-up times can be described by a normal model with a mean of 22 minutes and a standard deviation of four minutes. The typical worker needs five minutes to adjust to his or her surroundings before beginning duties. What percent of new machine set ups are completed within 25 minutes to allow for this? 77.3% The unemployment rate of persons with a disability is typically higher than for those with no disability. Recent statistics report that this rate is 14.5%. An advocacy group in a large city located in the southeastern region of the U.S. selected a random sample of 250 persons with a disability. What is the probability that no more than 30 persons in this sample are unemployed? 0.1314 The unemployment rate of persons with a disability is typically higher than for those with no disability. Recent statistics report that this rate is 14.5%. An advocacy group in a large city located in the southeastern region of the U.S. selected a random sample of 250 persons with a disability. What is the probability that at least 20 persons in this sample are unemployed? 0.9982 In a metal fabrication process, metal rods are produced to a specified target length of 15 feet. Suppose that the lengths are normally distributed. A quality control specialist collects a random sample of 16 rods and finds the sample mean length to be 14.8 feet and a standard deviation of 0.65 feet. Which of the following statement is true? The sampling distribution for the sample mean follows the t-distribution with 15 degrees of freedom In a metal fabrication process, metal rods are produced to a specified target length of 15 feet. Suppose that the lengths are normally distributed. A quality control specialist collects a random sample of 16 rods and finds the sample mean length to be 14.8 feet and a standard deviation of 0.65 feet. The standard error of the mean is 0.1625 ft. In a metal fabrication process, metal rods are produced to a specified target length of 15 feet. Suppose that the lengths are normally distributed. A quality control specialist collects a random sample of 16 rods and finds the sample mean length to be 14.8 feet and a standard deviation of 0.65 feet. The 95% confidence interval for the true mean length of rods produced by this process is 14.454 to 15.146 ft. A manufacturer of cheese filled ravioli supplies a pizza restaurant chain. Based on data collected from its automatic filling process, the amount of cheese inserted into the ravioli is normally distributed. To make sure that the automatic filling process is on target, quality control inspectors take a sample of 25 ravioli. The correct value of t* to construct a 99% confidence interval for the true mean amount of cheese filling is 2.797 A manufacturer of cheese filled ravioli supplies a pizza restaurant chain. Based on data collected from its automatic filling process, the amount of cheese inserted into the ravioli is normally distributed. To make sure that the automatic filling process is on target, quality control inspectors take a sample of 25 ravioli and measure the weight of cheese filling. They find a sample mean weight of 15 grams with a standard deviation of 1.5 grams. What is the margin of error at 90% confidence? .5133 grams Insurance companies track life expectancy information to assist in determining the cost of life insurance policies. ABI Insurance randomly sampled 100 recently paid policies and determined the average age of clients in this sample to be 77.7 years with a standard deviation of 3.6. The 90% confidence interval for the true mean age of its life insurance policy holders is 77.1 to 78.3 years Which of the following is not an assumption and/or condition required for constructing a confidence interval for the mean? Success/Failure A manufacturer of cheese filled ravioli supplies a pizza restaurant chain. Based on data collected from its automatic filling process, the amount of cheese inserted into the ravioli is normally distributed. To make sure that the automatic filling process is on target, quality control inspectors take a sample of 25 ravioli and measure the weight of cheese filling. They find the 99% confidence interval of 14.16 to 15.84 grams. Which of the following is the correct interpretation? We are 99% confident that the mean weight of cheese filling in all ravioli made by this process is between 14.16 and 15.84 grams All else being equal, increasing the level of confidence desired will increase the margin of error. In a metal fabrication process, metal rods are produced that have an average length of 20.5 feet with a standard deviation of 2.3 feet. A quality control specialist collects a random sample of 30 rods and measures their lengths. The sampling distribution of the sample mean lengths is normally distributed with a mean of 20.5 feet and standard deviation of 0.42. We can say this because the Central Limit theorem applies. In a metal fabrication process, metal rods are produced that have an average length of 20.5 feet with a standard deviation of 2.3 feet. A quality control specialist collects a random sample of 30 rods and measures their lengths. Suppose the resulting sample mean is 19.5 feet. Which of the following statements is true? This sample mean is 2.38 standard deviations below what we expect. In a metal fabrication process, metal rods are produced that have an average length of 20.5 feet with a standard deviation of 2.3 feet. A quality control specialist collects a random sample of 30 rods and measures their lengths. What is the probability of observing a sample mean greater than 21 feet? .1170 Grandma Gertrude's Chocolates, a family owned business, has begun making a new line of chocolates with high levels of cacao so it can advertise its health benefits of antioxidants. The product with the highest % cacao at Grandma Gertrude's Chocolates averages 45% cacao with a standard deviation of 6 %. Suppose a sample of 36 pieces of this chocolate is taken from the production line. What is the standard deviation of the sampling distribution of the sample mean? 1% Grandma Gertrude's Chocolates, a family owned business, has an opportunity to supply its product for distribution through a large coffee house chain. However, the coffee house chain has certain specifications regarding cacao content as it wishes to advertise the health benefits (antioxidants) of the chocolate products it sells. Suppose quality control inspectors at the coffee house chain take a sample of 100 pieces of this chocolate product from an incoming shipment. They find a sample average of 60% cacao with a sample standard deviation of 8%. What is the standard error of the sampling distribution of the sample mean? .8% A company manufacturing computer chips finds that 8% of all chips manufactured are defective. In an effort to decrease the percentage of defective chips, management decides to provide additional training to those employees hired within the last year. After training was implemented, a sample of 450 chips revealed only 27 defects. A hypothesis test is performed to determine if the additional training was effective in lowering the defect rate. Which of the following statement is true about this hypothesis test? It is a one tailed test about a mean. A company manufacturing computer chips finds that 8% of all chips manufactured are defective. In an effort to decrease the percentage of defective chips, management decides to provide additional training to those employees hired within the last year. After training was implemented, a sample of 450 chips revealed only 27 defects. A hypothesis test is performed to determine if the additional training was effective in lowering the defect rate. Suppose the P-value associated with the test statistic is 0.0594. At α = .01, we can conclude that the additional training did not significantly lower the defect rate. A company that sells eco-friendly cleaning products is concerned that only 19.5% of people who use such products select their brand. A marketing director suggests that the company invest in new advertising and labeling to strengthen its green image. The company decides to do so in a test market so that the effectiveness of the marketing campaign may be evaluated. In this context, committing a Type I error 1)occurs when they conclude that the percentage of customers purchasing the company's brand has increased when in fact it has not. 2)would result in the company wasting money on a new marketing campaign that does not increase the percentage of customers buying their brand A company that sells eco-friendly cleaning products is concerned that only 19.5% of people who use such products select their brand. A marketing director suggests that the company invest in new advertising and labeling to strengthen its green image. The company decides to do so in a test market so that the effectiveness of the marketing campaign may be evaluated. Based on data collected in the test market, the company constructed a 98% confidence interval for the proportion of all consumers who might buy their brand. The resulting interval is 16% to 28%. What conclusion should the company reach about the new marketing campaign? The data do not provide convincing evidence that the marketing campaign increases the percentage of customers for the company's products. Suppose that you are conducting a two tailed test using a Z score at the 0.01 level of significance. The correct critical value(s) to be used in drawing a conclusion is (are) ±2.575 A large software development firm recently relocated its facilities. Top management is interested in fostering good relations with their new local community and has encouraged their professional employees to engage in local service activities. They believe that the firm's professionals volunteer an average of more than 15 hours per month. If this is not the case, they will institute an incentive program to increase community involvement. The correct null and alternative hypotheses to test the belief of top management are H0 : μ = 15 and HA : μ > 15 A large software development firm recently relocated its facilities. Top management is interested in fostering good relations with their new local community and has encouraged their professional employees to engage in local service activities. They believe that the firm's professionals volunteer an average of more than 15 hours per month. If this is not the case, they will institute an incentive program to increase community involvement. A random sample of 24 professionals yields a mean of 16.6 hours and a standard deviation of 2.22 hours. The P-value associated with the resulting test statistic is 0.0009. At α = 0.05, which of the following is the correct conclusion? 1)We reject the null hypothesis 2)The firm shouldn't need to institute an incentive program because the evidence indicates that professional employees volunteer an average of more than 15 hours per month in their local community. A large software development firm recently relocated its facilities. Top management is interested in fostering good relations with their new local community and has encouraged their professional employees to engage in local service activities. They believe that the firm's professionals volunteer an average of more than 15 hours per month. If this is not the case, they will institute an incentive program to increase community involvement. Based on data collected they perform the appropriate hypothesis test. A Type II error in this context means 1)they failed to detect that the average number of hours volunteered by the firm's professional employees is more than 15 hours when in fact it is. 2) they would waste money instituting an incentive program to increase community involvement among its professional employees that was not needed.