Question

For students who first enrolled in two year public institutions in a recent​ semester, the proportion who earned a​ bachelor's degree within six years was 0.398 . The president of a certain college believes that the proportion of students who enroll in her institution have a lower completion rate. ​
(a) Determine the null and alternative hypotheses. ​
(b) Explain what it would mean to make a Type I error.
​(c) Explain what it would mean to make a Type II error.

Answer 1

Answer:

a) Null hypothesis: $p \geq 0.368$

Alternative hypothesis: $p$

b) A type of error I for this case would be reject the null hypothesis that the population proportion is greater or equal than 0.368 when actually is not true.

c) A type of error II for this case would be FAIL to reject the null hypothesis that the population proportion is greater or equal than 0.368 when actually the alternative hypothesis is the true.

Step-by-step explanation:

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.

Part a

On this case we want to test if the proportion of students who enroll in her institution have a lower completion rate (0.398), so the system of hypothesis would be:

Null hypothesis: $p \geq 0.368$

Alternative hypothesis: $p$

Part b

A type of error I for this case would be reject the null hypothesis that the population proportion is greater or equal than 0.368 when actually is not true.

Part c

A type of error II for this case would be FAIL to reject the null hypothesis that the population proportion is greater or equal than 0.368 when actually the alternative hypothesis is the true.