. A production manager claims that an average of 50 boxes per hour is filled with finished goods at the final stage of a production line. A random sampling of 48 different workers, at different times, working at the end of identical production lines shows an average number of boxes filled as 47.5 with a standard deviation of 0.7 boxes. Does this evidence support the claim by the production manager at the 5% significance level? Historically, evening long-distance calls from a particular city have averaged 15.2 minutes per call. In a random sample of 35 calls, the sample mean time was 14.3 minutes. Assume the standard deviation is known to be 5 minutes. Using a 0.05 level of significance, is there sufficient evidence to conclude that the average evening long-distance call has decreased? A sample of 90 people was selected from a large population. If the average amount spent per week on lottery tickets was found to be 5.60 and the sample standard deviation was 2.90, calculate the 95% confidence interval for the mean of the population. . A random sample of 300 items from a production line is selected for testing to estimate their average length of life. The sample mean was calculated to be 250 hours and the sample standard deviation found to be 6 hours. Calculate the 95% and 99% confidence intervals for the population mean. A random sample of 100 invoices has been selected from a large file of company records. If nine were found to contain errors, calculate a 95% confidence interval for the true percentage of invoices from this company containing errors. An importer has ordered a large shipment of tomatoes. When it arrives he examines a randomly chosen sample of 50 boxes and finds that 12 contain at least one bad tomato. Assuming that these boxes may be regarded as being a random sample from the boxes in the shipment, obtain a 99% confidence interval for the proportion of boxes containing at least one bad tomato, giving your confidence limits correct to three rlcmimnl nlnrn