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I'm not sure that I'm understanding this stuff fully so I would appreciate it if someone could check my work.

QUESTION The percentage of children who leave foster care due to adoption is generally accepted to be 15%. A social worker claims that this percent is incorrect. After performing a hypothesis test on his claim using sample data from 2009, he fails to reject the null hypothesis. According to a report by the US department of Health and Human Services, the actual percentage of children who left foster care due to adoption was 20% in 2009. Was an error made? If so, what type?

MY ANSWER Ho = p=15% Ha = pā‰ 15%

Ho is proven to be false, but it says that the service worker doesn't reject it. Since they think the Ho is true when it isn't, this is a type 1 error.

user354704
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  • A type 1 error related to the significance level which is used to determine whether or not the null hypothesis should be rejected. (not rejecting the null hypothesis but you should have). Since this is related to the $p$ of the null hypothesis it looks like in your case that this involves indeed a type 1 error. ā€“ imranfat Jul 18 '16 at 04:30
  • Apparently the back of my book includes some answers. It actually says that it is a type II error. ā€“ user354704 Jul 18 '16 at 04:37
  • You are right. My argument is correct but instead of type 1 I should have mentioned type 2. It is clearly explained here: https://en.wikipedia.org/wiki/Type_I_and_type_II_errors#Type_I_error ā€“ imranfat Jul 18 '16 at 04:40

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