Question 1 – A manufacturing company produces electrical insulators. If the insulators break when is use, a short circuit is likely to occur. To test the strength of the insulators, destructive testing is carried out to determine how much force is required to break the insulators. The force is measured by observing the number of pounds of force applied to the insulator before it breaks. The following data are from a random sample of 28 insulator subjected to this testing. 1870 1728 1656 1610 1634 1784 1522 1696 1592 1662 1866 1764 1734 1662 1734 1774 1550 1756 1762 1866 1820 1744 1788 1688 1810 1752 1680 1810 a) At the 0.5 level of significance, is there evidence that the population mean force required to break the insulator is greater than 1700 pounds? Clearly show the steps of the hypothesis test that you use, and express your final conclusion using a clear English sentence. b) What assumption about the population distribution is needed in order to conduct the test in (a)? c) Calculate the 98% confidence interval for the population mean force required to break the insulator. Question 2 – The Peabody Research Centre conducted a survey of adults, aged 18 years and older, that included 1,954 cellphone owners. The survey found that 1,016 of adult cellphone owners use their phone while watching TV. The authors of the article claim that the survey proves that more than half of all adult cellphone users use their phone while watching TV. a) Test the claim of the authors using a significance level of 0.05. Clearly show the steps of the hypothesis test that you use, and express your final conclusion using a clear English sentence. b) One year later the Peabody Research Centre wants to perform a survey to see if the percentage of adult cellphone owners who use their phone while watching TV has changed. How many adult cellphone users must be in the new survey to obtain the percentage within 3%, and with a level of confidence of 0.97? c) Calculate the 96% confidence interval for the percentage of adult cellphone users who use their phone while watching TV. Question 3 – The quality-control manager at a compact fluorescent light bulb (CFL) manufacturer needs to determine whether the mean life of a large shipment of CFLs is equal to 7,500 hours. The population standard deviation is 1,000 hours. a) How large a sample should be manager use to assess the mean lifetime of the population of CFLs, to within 250 hours, and at a level of confidence of 0.95? b) The quality-control manager uses a random sample of 64 CFLs and obtains a mean life of 7,250 hours. Is there evidence that the mean life is different from 7,500 hours? Use a level of significance of 0.05. Clearly show the steps of the hypothesis test that you use, and express your final conclusion using a clear English sentence. DO NOT use the pvalue method for this question. c) Calculate the 90% confidence interval for the mean life of the CFLs. What is the margin of error
