Question

Determine both Type$\mathrm{I}$and Type$\mathrm{II}$errors for the following scenario:

Assume a null hypothesis,${\mathrm{H}}_0$, that states the percentage of adults with jobs is at least $88\%$.

Identify the Type$\mathrm{I}$and Type $\mathrm{II}$errors from these four statements.

a. Not to reject the null hypothesis that the percentage of adults who have jobs is at least $88\%$when that percentage is actually less than $88\%$

b. Not to reject the null hypothesis that the percentage of adults who have jobs is at least $88\%$when the percentage is actually at least $88\%$.

c. Reject the null hypothesis that the percentage of adults who have jobs is at least $88\%$when the percentage is actually at least $88\%$.

d. Reject the null hypothesis that the percentage of adults who have jobs is at least $88\%$when that percentage is actually less than $88\%$.

Short answer

Type one error is,

d. Reject the null hypothesis that the percentage of adults who have jobs is at least $88\%$when that percentage is actually less than $88\%$.

Type two error is,

a. Not to reject the null hypothesis that the percentage of adults who have jobs is at least $88\%$when that percentage is actually less than$88\%$.

Step-by-step solution

Introduction

When the null hypothesis is true, a type one error is defined as rejecting it.

When the null hypothesis is incorrect, a type two mistake occurs when the null hypothesis is not rejected.

Explanation 

Type$\mathrm{I}$error is,

Reject the null hypothesis that the percentage of adults with jobs is less than 88 percent when it is actually greater than $88$percent.

Type$\mathrm{II}$error is,

Not to reject the null hypothesis that the proportion of adults with jobs is at least $88$percent when the proportion is actually less than $88$percent.