In the following questions we will explore which hypothesis we should test and t
ID: 3150935 • Letter: I
Question
In the following questions we will explore which hypothesis we should test and then we will look at what type of error is worse, Type I or Type II, and which error is worst, depending upon circumstances.
(b) Assuming that the correct alternative hypothesis is that the defendant it guilty, which type of error will have worse consequences in a murder trial with the death penalty a real possibility if there is a conviction?
Type I, because it mean a guilty person goes free.
Type II, because it means a guilty person goes free.
Type I, because it means an innocent person is put to death.
Type II, because it means an innocent person is put to death.
(c) A manufacturer of cereal has a production plant devoted to filling cereal boxes with raisen bran. The company advertises that each box will contain more than 1/2 cup of raisens. For each production run, the manufacturer takes a SRS of cereal boxes to make sure that the average cups of raisens per box is more than 1/2 cup. If the average cups of raisens of the cereal box is 1/2 cup or less, the production run is halted at great cost to the company so that the amount of raisens put in a box can be increased. Suppose that the alternative hypothesis being tested by the company is: "the average number of cups of raisens per box is more than 1/2". Which type of error will have worse consequences to the company?
Type I because it means that, on average, 1/2 or fewer cups of raisens are in the cereal boxes and the company's advertising will be wrong.
Type II because it means that, on average, 1/2 or fewer cups of raisens are in the cereal boxes and the company's advertising will be wrong.
Type I because it means the production run will be halted when it doesn't have to bebecause there really more than 1/2 cup of raisens per box.
Type II because it means the production run will be halted when it doesn't have to be because there really are on average more than 1/2 cup of raisens per box.
Explanation / Answer
(b)
Here the null hypothesis is H0: the defendant is not guilty
and the alternative hypothesis is H1: the defendent is guilty.
Type I error is rejecting H0 when it is true i.e. the defendant is put to death although he is innocent.
Type II error is accepting H0 when it is false i.e. defendant is set free although he is guilty.
From sociological point of view, in this case type I error is worse i.e. an innocent person is put to death.
Hence option 3."Type I, because it means an innocent person is put to death" is worse.
(c)
Let p be the proportion of raisen in a cereal box.
The null hypothesis is H0: p=1/2
against the alternative hypothesis H1:p>1/2.
Type I error is rejecting H0 when it is true i.e. a box with lower raisen quantity passes the quality test.
Type II error is accepting H0 when it is false i.e. a box with good raisen quality does not passes the quality test.
Here for type II error, for a good box the production process is halted at great cost. Here type II error is worse.
Hence option 4. "Type II because it means the production run will be halted when it doesn't have to be because there really are on average more than 1/2 cup of raisens per box" is worse.
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