A coin-operated coffee machine made by BIG Corporation was designed to discharge a mean of 6.9 ounces of coffee per cup. If it dispenses more than that on average, the corporation may lose money, and if it dispenses less, the customers may complain. Believing that the mean amount of coffee μ dispensed by the machine is less than 6.9 ounces, BIG plans to do a statistical test of the claim that the machine is working as designed. BIG gathers a random sample of 125 amounts of coffee dispensed by the machine. Suppose that the population of amounts of coffee dispensed by the machine has a standard deviation of 0.7 ounces and that BIG performs its hypothesis test using the 0.1 level of significance. Based on this information, answer the questions below. Carry your intermediate computations to at least four decimal places, and round your responses as indicated. (a) What are the null and alternative hypotheses that BIG should use for the test? (b) What is the probability that BIG commits a Type I error? Round your response to at least two decimal places. (c) Assuming that the actual value of µ is 6.79 ounces, what is the probability that BIG rejects the null hypothesis? Round your response to at least two decimal places. (d) Suppose that BIG decides to perform another statistical test using the same population, the same null and alternative hypotheses, and the same sample size, but for this second test BIG uses a significance level of 0.05 instead of a significance level of 0.1. Assuming that the actual value of µ is 6.79 ounces, how does the probability that BIG commits a Type II error in this second test compare to the probability that BIG commits a Type II error in the original test?
A coin-operated coffee machine made by BIG Corporation was designed to discharge a mean of 6.9...
A coin-operated coffee machine made by BIG Corporation was designed to discharge a mean of 7.1 ounces of coffee per cup. If it dispenses more than that on average, the corporation may lose money, and if it dispenses less, the customers may complain. Believing that the mean amount of coffee dispensed by the machine, , is different from 7.1 ounces, BIG plans to do a statistical test of the claim that the machine is working as designed. Technicians gather a...
A coin-operated coffee machine made by BIG Corporation was designed to discharge a mean of 7.2 ounces of coffee per cup. If it dispenses more than that on average, the corporation may lose money, and if it dispenses less, the customers may complain. Believing that the mean amount of coffee dispensed by the machine, H, is less than 7.2 ounces, BIG plans to do a statistical test of the claim that the machine is working as designed. Technicians gather a...
A coin-operated coffee machine made by BIG Corporation was designed to discharge a mean of eight ounces of coffee per cup. If it dispenses more that that on average, the corporation may lose money, and if it dispenses less, the customers may complain BIG Corporation would like to estimate the mean amount of coffee, H, dispensed per cup by this machine. BIG will choose a random sample of cup amounts dispensed by this machine and use this sample to estimate...
A coin operated coffee machine made by BIG Corporation was designed to discharge amean of eight ounces of coffee Cup It dispenses more than that on average, the corporation may lose money, and it dispenseless, the customers complain BIG Corporation would like to estimate the mean amount of coffee dispensed per cup by this machine BIG wil choose a random sample of cup amounts dispersed by this machine and use the sample tom ate Assuming that the standard deviation of...
A coin-operated drink machine was designed to discharge a mean of 7 ounces of coffee per cup. In a test of the machine, the discharge amounts in 21 randomly chosen cups of coffee from the machine were recorded. The sample mean and sample standard deviation were 6.84 ounces and 0.3 ounces, respectively. If we assume that the discharge amounts are normally_distributed, is there enough evidence, at the 0.1 level of significance, to conclude that the true mean discharge, μ, differs...
A coin-operated drink machine was designed to discharge a mean of 9 ounces of coffee per cup. In a test of the machine, the discharge amounts in 16 randomly chosen cups of coffee from the machine were recorded. The sample mean and sample standard deviation were 8.85 ounces and 0.25 ounces, respectively. If we assume that the discharge amounts are normally distributed, is there enough evidence, at the 0.1 level of significance, to conclude that the true mean discharge, H,...
A coin-operated drink machine was designed to discharge a mean of 7 ounces of coffee per cup, In a test of the machine, the discharge amounts in 14 randomly chosen cups of coffee from the machine were recorded. The sample mean and sample standard deviation were 6.96 ounces and 0.12 ounces, respectively. If we assume that the discharge amounts are normally distributed, is there enough evidence, at the 0.05 level of significance, to conclude that the true mean discharge, H,...
A coin-operated drink machine was designed to discharge a mean of 8 ounces of coffee per cup. In a test of the machine, the discharge amounts in 21 randomly chosen cups of coffee from the machine were recorded. The sample mean and sample standard deviation were 7.87 ounces and 0.23 ounces, respectively. If we assume that the discharge amounts are normally distributed, is there enough evidence, at the 0.05 level of significance, to conclude that the true mean discharge, ?,...
A coin-operated drink machine was designed to discharge a mean of 8 ounces of coffee per cup. In a test of the machine, the discharge amounts in 14 randomly chosen cups of coffee from the machine were recorded. The sample mean and sample standard deviation were 8.02 ounces and 0 26 ounces, respectively. If we assume that the discharge amounts are normally distributed, is there enough evidence, at the 0.05 level of significance, to conclude that the true mean discharge,...
A coin operated drink machine was designed to discharge a mean of 7 ounces of coffee per cup. In a test of the machine, the discharge amounts in 14 randomly chosen cups of coffee from the machine were recorded. The sample mean and sample standard deviation were 7.02 ounces and 0.24 ounces, respectively. If we assume that the discharge amounts are normally distributed, is there enough evidence, at the 0.05 level of significance, to conclude that the true mean discharge,...