Prisoners convicted for stealing cars used to serve Y years in prison, where the probability density function (pdf) of Y was of the form: fy(y) = y², 0≤ y ≤ 3. However, recent judicial reforms may have changed the distribution of Y. A review of 50 individuals convicted for this crime, ago showed that 8 served less than one year in jail, 16 served between one and two years, and 26 served between two and three years. (i) Are these data consistent with the pdf fy(y)? Do an appropriate hypothesis test and indicate what the smallest level of significance is such that Ho can be rejected. How do you call this smallest level of significance? For which range of a, Ho would be accepted or rejected?

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Prisoners convicted for stealing cars used to serve Y years in prison, where the probability density
function (pdf) of Y was of the form:
fy(y) = y², 0≤ y ≤ 3.
However, recent judicial reforms may have changed the distribution of Y. A review of 50 individuals
convicted for this crime, ago showed that 8 served less than one year in jail, 16 served between one
and two years, and 26 served between two and three years.
(i) Are these data consistent with the pdf fy(y)? Do an appropriate hypothesis test and
indicate what the smallest level of significance is such that Ho can be rejected.
How do you call this smallest level of significance? For which range of a, Ho would be
accepted or rejected?
Transcribed Image Text:Prisoners convicted for stealing cars used to serve Y years in prison, where the probability density function (pdf) of Y was of the form: fy(y) = y², 0≤ y ≤ 3. However, recent judicial reforms may have changed the distribution of Y. A review of 50 individuals convicted for this crime, ago showed that 8 served less than one year in jail, 16 served between one and two years, and 26 served between two and three years. (i) Are these data consistent with the pdf fy(y)? Do an appropriate hypothesis test and indicate what the smallest level of significance is such that Ho can be rejected. How do you call this smallest level of significance? For which range of a, Ho would be accepted or rejected?
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