Question 8 of 10 , Step 1 of 7
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1
A local police chief claims that $43 \%$ of all drug-related arrests are never prosecuted. A sample of 900 arrests shows that $40 \%$ of the arrests were not prosecuted. Using this information, one officer wants to test the claim that the number of arrests that are never prosecuted is under what the chief stated. Is there enough evidence at the 0.02 level to support the officer's claim?
Step 1 of 7 : State the null and alternative hypotheses.
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Final Answer: The null hypothesis (H0) is that the proportion of all drug-related arrests that are never prosecuted is 43% (p = 0.43). The alternative hypothesis (H1) is that the proportion is less than 43% (p < 0.43).
Step 1 ：The null hypothesis is the statement that the parameter takes the value stated in the null hypothesis under the assumption that the null hypothesis is true. In this case, the null hypothesis is that the proportion of all drug-related arrests that are never prosecuted is 43%, as claimed by the police chief.
Step 2 ：The alternative hypothesis is the statement that the parameter takes a value that contradicts the null hypothesis. In this case, the alternative hypothesis is that the proportion of all drug-related arrests that are never prosecuted is less than 43%, as the officer wants to test.
Step 3 ：So, the null and alternative hypotheses are: Null hypothesis (H0): p = 0.43 Alternative hypothesis (H1): p < 0.43 where p is the proportion of all drug-related arrests that are never prosecuted.
Step 4 ：Final Answer: The null hypothesis (H0) is that the proportion of all drug-related arrests that are never prosecuted is 43% (p = 0.43). The alternative hypothesis (H1) is that the proportion is less than 43% (p < 0.43).
