Suppose that we wish to test the null hypothesis H 0 that the proportion p , of
ID: 3324907 • Letter: S
Question
Suppose that we wish to test the null hypothesis H0 that the proportion p, of ledger sheets with errors is equal to 0.05 versus the alternative H1, that the proportion is larger than 0.05, by using the following scheme. Two ledger sheets are selected at random. If both are error free, we reject H0. If one or more contains an error, we look at a third sheet. If the third sheet is error free, we reject H0. In all other cases, we accept H0.
In terms of this problem, what is a type I error?
What is the value of associated with this test?
In terms of this problem, what is a type II error?
Explanation / Answer
In terms of this problem, what is a type I error?
Answer:
We know that type I error is the error or probability of rejecting null hypothesis H0 when it is true. For the given scenario, type I error is defined as the probability or error occurred when we reject the null hypothesis that the proportion p of ledger sheets with errors is equal to 0.05; however actual proportion of ledger sheets with errors is 0.05.
What is the value of associated with this test?
Answer:
For the given scenario, the value of or level of significance is not given. In this type of cases, we consider the default level of significance or alpha value as 5% or = 0.05.
In terms of this problem, what is a type II error?
Answer:
We know that type II error is defined as the probability of do not rejecting the null hypothesis even though it is not true. For the given scenario, type II error is the probability of do not rejecting the null hypothesis that the proportion p of ledger sheets with errors is equal to 0.05; however actual proportion of ledger sheets with errors is greater than 0.05.
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