1. For this problem, you will use the confidence interval to make a decision and answer the question. A company manufactures light bulbs. The company wants the bulbs to have a mean life span of 1000 hours. This average is maintained by periodically testing random samples of 16 light bulbs. A sample of 16 light bulbs is randomly selected and tested. The mean life span of the sample is 1015 hours and the standard deviation is 25 hours. Assume the life spans are approximately normally distributed.
   1. Construct a 99% confidence interval:
   2. Does the confidence interval contain the value 1000g, the mean target life span the company wants?
   3. Based on the confidence interval, is there convincing evidence to conclude that the company is making acceptable light bulbs? Explain your answer:
4. The National Highway Traffic Safety Administration conducted crash tests of child booster seats for cars. Listed below are results from those tests, with the measurements given in hic (standard head injury condition units). The safety requirement is that the hic measurement should be less than 1000 hic. Use a 0.01 significance level to the claim that the sample is from a population with a mean less than 1000 hic. Do the results suggest that all of the child booster seats meet the specified requirement? Assume that the original population is normally distributed (this does not mean you are using the z-test!). 774 649 1210 546 431 612
   1. Null hypothesis:
   2. Alternative hypothesis:
   3. Test statistic:
   4. Critical value(s) and region(s); sketch the distribution:
   5. P-value:
   6. The 99% Confidence interval:
   7. Conclusion: State whether you are accepting or rejecting the null. ALSO TO BE SURE TO ADDRESS THE ORIGINAL CLAIM/QUESTION. BEING WORDY IS O.K.
   8. Basedonwhetheryoufailedtorejectthenullhypothesisorrejectedthenullhypothesis,whattypeoferrormighthavebeencommitted,aTypeIerrororaTypeIIerror?Explain.