Question

The mean length of imprisonment for motor vehicle theft offenders in this country is 22.1 months. A hypothesis test is to be performed to decide whether the mean lot of imprisonment in this oyers from the national mean. The null and ternative hypotheses are = 22.1 months H 2 2.1 months a. Explain what would mean to make a type error OA Alypel error would occur if in fact - 22.1 months, but the results of the sampling lead to the conclusion that 221 months OB Atype 1 error would occur in fact 22.1 months, but the results of the sampling to lead to the conclusion that 22 months OC Atype error would occur in fact 22.1 months but the results of the camping fail to lead to the conclusion that 22.1 months b. Explain what it would mean to make a type ilerror OA Atype it error would occur in fact OB Atype ilerror would occur if in fact OC A type it error would occur in fact 22 months, but the results of the samling lead to the con t rat 22 months 22.1 months, but the results of the samling ad to the conclusion that 2 months 22.1 months, but the results of the sampling fail to bad to the conclusion that 22. 1 months c. Explain what it would mean to make a correct decision A Artrinn w ir months and then the Click to select your answer

Answer 1

Type I error in a hypothesis testi tovor in a hepothesis testing is the rejection of a true null hypothesis - here null hypothesis is that Me 22•1 - If our test using the sample data leads us to deject the hull hypothesis Ci.e pe-22.1) when in fact the mean length of impoisonment in the city is equal to the national mean ciell= 22.1 then we will be committing a type 2 error, so when we commit a type I caror - we reject the neel hypothesis when in fact it is true and we accept the alternative hypothesis which is false. es Option A is correct A type 1 eroor would occur if in fact Mz22-1 months, but the results of the sampling lead to the conclusion that p +221 months O Type exsov in hypothesis testing is not rejecting a null hypothesis which is in fact false. In this case when in fact u72201 and the samplerig results lead us to accept that M=221 (null hy pothesis) it is a type Terror, 3. By comitting type B cover we accept a false neell hypothesis and geject a true alternatine heypothesis. 6. Ansever is option - A type I error occur if in jack 4 # 22. months but the results of the sampling fail to lead to the conclusion that M+22. 1 months Correct decision is accepting the null hypothesis when it is true and rejecturing when it is felse, boboichrsson ; Answer is option - A correct decision is would occur if m= 22.1 months and the results of sampling do not lead to the rejection of that fact; or if u €22.1 months and the results of the sampling leads to that conclusion. @ Given that results leads to non-rejection of null hypothesis (ie null accepted) and in fact length of a motor vehicle theft offenders in the city equals to national mean of 22.1 (ie M=2201; nullis true) - Therefore null accepted at null is true - Correct Decision Colt leads to non rejection of the null hypothesis (null accepled) and in fact por vehicle theft imprisonment length in the city is differs from the natione Sloom me national 129.1 months Cie Mt 2001, nullis false) - Here we accepted a tal null hypothesis - Type I error U mean of all.) months' Cie MF