Assignment 4 l. The director of manufacturing at a clothing factory needs to determine whether a new machine is producing a particular type of cloth according to the manufacturer's specications, which indicate that the cloth should have a mean breaking strength of 70 pounds and a standard deviation of 3.5 pounds. The director is concerned that if the mean breaking strength is actually less than 70 pounds, the company will face too many lawsuits. A sample of 49 pieces reveals a sample mean of 69.] pounds. a. State the null and alternative hypotheses b. At the 5% level of significance. is there evidence that the mean breaking strength is less than 70 pounds? 2. A machine being used for packaging seedless golden raisins has been set so that. on average, 15 ounces of raisins will be packaged per box. The operations manager wishes to te st the machine setting and selects a sample of 20 consecutive raisin packages lled during the production process. The sample mean and sample standard deviation are l5.I ounces and 0.4 ounces respectively. a. State the null and alternative hypotheses b. At the 1% level of significance, is there evidence that the mean weight per box is different from 15 ounces? 3. The personnel director of a large insurance company is interested in reducing the turnover rate of data processing staff in the rst year of employment. Past records indicate that 25% of all new hires in this area are no longer employed at the end of 1 year. Extensive new training approaches are implemented for a sample of ISO new data processing staff. At the end ofa 1-year period, 9 ofthis 150 individual are no longer employed. a. State the null and alternative hypotheses b. At the 5% level of signicance, is there evidence that the proportion of data processing staff who have gone through the new training and are no longer employed is less than 25%