Question

the null hypothesis, h0, is: no more than 90% of homes in the city are up to the current electric codes. and the alternative hypothesis, ha, is: an electrician claims more than 90% of homes in the city are up to the current electric codes.

Answer 1

"β", the probability of a type II error here in this question is, the electrician cannot conclude that more than 90% of homes in the city are up to the current electric codes when, in fact, more than 90% of homes are up to the current electric codes.

As per the question statement, the null hypothesis, $H_{o}$, is that, no more than 90% of homes in the city are up to the current electric codes, while an alternative hypothesis, $H_{a}$, is by an electrician claiming more than 90% of homes in the city are up to the current electric codes.

We are required to find out "β" which is the probability of a type II error.

β = Probability of accepting $H_{o}$ when it is incorrect.

The probability of a Type II error occurs in the situation where, the null hypothesis $H_{o}$ of "more than 90% of homes in the city are up to the current electric codes" is accepted even though the alternative hypothesis that the electrician claims about "more than 90% of homes in the city being up to the current electric codes" is true. More clearly, the alternative hypothesis that the electrician claims about more than 90% of homes in the city being up to the current electric codes is in fact, rejected when it is correct.

Hence the correct answer :

The probability of Type II error is (β) is that, "The electrician cannot conclude that more than 90% of homes in the city are up to the current electric codes when, in fact, more than 90% of homes are up to the current electric codes".

• Probability: In Mathematics, Probability is the extent to which an event is likely to occur, measured by the ratio of the favorable cases to the whole number of cases possible.
• Null & Alternative Hypothesis: A null hypothesis is a type of statistical hypothesis that proposes that no statistical significance exists in a set of given observations while, an alternative hypothesis states about our research prediction of an effect or relationship.

To learn more about Null & Alternative Hypothesis, click on the link below.

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