Question

Identify the type I error and the type II error that correspond to the given hypothesis.

The percentage of households with more than 1 pet is = to 65 %.
Identify the type I error.
A. Reject the null hypothesis that the percentage of households with more than 1 pet is equal to 65 % when that percentage is actually different from 65 %.
B. Fail to reject the null hypothesis that the percentage of households with more than 1 pet is equal to 65 % when that percentage is actually different from 65 %.
C. Fail to reject the null hypothesis that the percentage of households with more than 1 pet is equal to 65 % when the percentage is actually equal to 65 %.
D. Reject the null hypothesis that the percentage of households with more than 1 pet is equal to 65 % when that percentage is actually equal to 65 %.

Answer 1

Type I error would be that we conculde to reject the null hypothesis that the percentage of households with more than 1 pet is equal to 65 % when that percentage is actually equal to 65%.

Type II error would be that we fail to reject the null hypothesis that the percentage of households with more than 1 pet is equal to 65 % when that percentage is actually different from 65%.

Explanation:

We are given that the percentage of households with more than 1 pet is 65%.

Let p = population % of households with more than 1 pet

So, Null Hypothesis,
`H_0` : p = 65% {means that the percentage of households with more than 1 pet is equal to 65 %}

Alternate Hypothesis,
`H_A` : p
`\\eq` 65% {means that the percentage of households with more than 1 pet is different from 65 %}

Type I error states that the null hypothesis is rejected given the fact that null hypothesis was true. Or in other words, it is the probability of rejecting a true hypothesis.

So, in our case, type I error would be that we conculde to reject the null hypothesis that the percentage of households with more than 1 pet is equal to 65 % when that percentage is actually equal to 65%.

Type II error states that the null hypothesis is accepted given the fact that null hypothesis was false. Or in other words, it is the probability of accepting a false hypothesis.

So, in our case, type II error would be that we fail to reject the null hypothesis that the percentage of households with more than 1 pet is equal to 65 % when that percentage is actually different from 65%.