Question

1.The US justice system considers an accused person innocent until proven guilty and there has to be proof beyond a reasonable doubt to convict the accused. In recent years, several individuals have been released from prison because new DNA tests proved them innocent. When the court originally convicted them (falsely as it turns out): (check all that apply)

	a.	They committed a type-II error
	b.	They committed both a type-I and a type-II error
	c.	They committed a type-I error
	d.	They committed neither a type-I nor a type-II error

2.In hypothesis testing, a Type 2 error occurs when (check all that apply)

	a.	The null hypothesis is not rejected when the null hypothesis is true.
	b.	The null hypothesis is rejected when the alternative hypothesis is true.
	c.	The null hypothesis is not rejected when the alternative hypothesis is true.
	d.	The null hypothesis is rejected when the null hypothesis is true.

3.Null and alternative hypotheses are statements about: (check all that apply)

	a.	population parameters.
	b.	sample parameters.
	c.	sample statistics.
	d.	it depends - sometimes population parameters and sometimes sample statistics.

Answer 1

1.Answer is (c) They committed type 1 error .

Note :Type 1 error is the error of rejecting a true null hypothesis

Type 2 error is the error of accepting a false null hypothesis

Null hypothesis is the hypothesis of no difference

In justice system the null hypothesis is : The accused is not guilty

Therefore , when the court originally convicted them ,that means they rejected the null hypothesis , they committed type 1 error .

2. answer is (c) The null hypothesis is not rejected when the alternative hypothesis is true .

Note : Alternative hypothesis is true means null hypothesis is false .Type 2 error is the error of accepting (or not rejecting a false null hypothesis) a false null hypothesis .

3. Answer is a) population parameters

Note :For example , in tests for mean , null hypothesis is

where is the population mean

Alternative hypothesis are

or   or