The production of a nationally marketed detergent results in certain workers receiving prolonged exposures to a...

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The production of a nationally marketed detergent results incertain workers receiving prolonged exposures to a Bacillussubtilis enzyme. Nineteen workers were tested to determine theeffects of those exposures, if any, on various respiratoryfunctions. One such function, airflow rate, is measured bycomputing the ratio of a personâ€™s forced expiratory volume (FEV) tohis or her vital capacity (VC). (Vital capacity is the maximumvolume of air a person can exhale after taking as deep a breath aspossible; FEV is the maximum volume of air a person exhale in onesecond.) In persons with no lung dysfunction, the â€œnormâ€ for FEV/VCratios is 0.80. Assume that the FEV/VC ratios are known to benormally distributed. For the 19 workers in the study, the meanFEV/VC ratio was 0.766 with standard deviation 0.0859. a. Based onyour result, is it believable that exposure to Bacillus subtilisenzyme has no effect on the FEV/VC ratio? Please compute thep-value for the test in two different ways: (i) assuming Ïƒ = 0.09and (ii) assuming Ïƒ is unknown. b. Based on this data, is itbelievable that Ïƒ = 0.09 ? Conduct a hypothesis test to answer thisquestion.

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a Let be the true FEVVCratios in workers having exposure to Bacillus subtilis enzymeWe want to test if exposure to Bacillus subtilis enzyme hasno effect on the FEVVC ratio the norm forFEVVC ratios being 080 That is we want to test if is equal to080The hypotheses areWe have the following sample informationn19 is the sample sizeis the sample mean FEVVC ratio among 19 workersis the sample standard deviation ofFEVVC ratio among19 workersis the hypothesized value of mean FEVVC ratio among the exposedfrom the null hypothesisi We know the population standard deviationofFEVVC ratioThe standard error of mean isSince we know the population standard deviation we will usenormal See Answer

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