Question: In the past, defendants convicted of grand theft auto served Y years in prison, where the pdf describing the variation in Y had the form

In the past, defendants convicted of grand theft auto served Y years in prison, where the pdf describing the variation in Y had the form
fY(y) = 1/9 y2, 0 < y ≤ 3
Recent judicial reforms, though, may have impacted the punishment meted out for this particular crime. A review of 50 individuals convicted of grand theft auto five years 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. Are these data consistent with fY(y)? Do an appropriate hypothesis test using the α = 0.05 level of significance.

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