Question

An ABC News/Washington Post poll conducted March 3-6, 2016 asked, "Would you support or oppose an effort made by the federal government to deport all 11 million undocumented immigrants and send them back to their home countries?" 36% of respondents said "Support." You wonder whether this percentage is actually higher, after the recent debate coverage of this issue. The following hypotheses were used :

If a Type II error was made when performing the test, what happened? (Select all correct choices.)

Group of answer choices

Your suspicions were correct, but the test results said otherwise.

Your suspicions were not correct, but the test results confirmed your suspicions.

You believe  but in reality, it is less than or equal to 0.36

You believe  but in reality it is greater than 0.36

It is impossible to answer without sample data.

Answer 1

Solution:

From given , we first write the null and alternative hypothesis are

H₀ : p = 0.36 vs H₁ : p > 0.36

We know that

Type I error : Reject the null hypothesis when the null hypothesis is true.

Type II error : Fail to reject the null hypothesis , when in fact , the the null hypothesis is NOT true.

So , for given problem Type II error ,

Your suspicions were not correct, but the test results confirmed your suspicions.

You believe p = 0.36  but in reality it is greater than 0.36