The cdc national estimates that 1 in 68 = 0.0147 children are diagnosed with have been diagnosed with autism spectrum disorder (asd). a researcher believes that the proportion children in their county is different from the cdc estimate. the hypotheses are sub(h,0): p=0.0147 sub(h,1): p≠0.0147. what is a type ii error in the context of this problem?

Null hypothesis:

Alternative hypothesis:

A type of error II for this case would be FAIL to reject the null hypothesis that the population proportion is equal to 0.0147 when actually the alternative hypothesis is true (the true proportion is different from 0.0147).

Step-by-step explanation:

Previous concepts

A hypothesis is defined as "a speculation or theory based on insufficient evidence that lends itself to further testing and experimentation. With further testing, a hypothesis can usually be proven true or false".  

The null hypothesis is defined as "a hypothesis that says there is no statistical significance between the two variables in the hypothesis. It is the hypothesis that the researcher is trying to disprove".  

The alternative hypothesis is "just the inverse, or opposite, of the null hypothesis. It is the hypothesis that researcher is trying to prove".  

Type I error, also known as a “false positive” is the error of rejecting a null  hypothesis when it is actually true. Can be interpreted as the error of no reject an  alternative hypothesis when the results can be  attributed not to the reality.  

Type II error, also known as a "false negative" is the error of not rejecting a null  hypothesis when the alternative hypothesis is the true. Can be interpreted as the error of failing to accept an alternative hypothesis when we don't have enough statistical power.  

Solution to the problem

On this case we want to test if the proportion of children diagnosed with Autism Spectrum Disorder (ASD) is different from 0.0147, so the system of hypothesis would be:

Null hypothesis:

Alternative hypothesis:

A type of error II for this case would be FAIL to reject the null hypothesis that the population proportion is equal to 0.0147 when actually the alternative hypothesis is true (the true proportion is different from 0.0147).

boxplot