Question

The mean price of mid-sized cars in a region is $32,000. A test is conducted to see if the claim is true. State the Type I and Type II errors in complete sentences.

Short answer

Type I error : Rejection of the null hypothesis even if it's correct.

Type II error : No rejection of the alternative hypothesis even if it's false.

Step-by-step solution

introduction

Given,

The mean price of mid-sized cars in a region is$\mathrm{\$}32,000$.

explanation

In the case of the null hypothesis we have,

${\mathrm{H}}_0:\mu =\mathrm{\$}32,000$which implies the mean price of the of mid-sized cars in a region is$\mathrm{\$}32,000$.

In the case of the alternative hypothesis we have,

${\mathrm{H}}_1:\mu \ne \mathrm{\$}32,000$which implies the mean price of the of mid-sized cars in a region is not $\mathrm{\$}32,000$.

Hence we get,

Type I error : Rejection of the null hypothesis even if it's correct.

Type II error : No rejection of the alternative hypothesis even if it's false.