Answer

Verified

373.8k+ views

**Hint:**We first express the concept of type 1 error and type 2 error probabilities. Then we state the theorems for calculating the probabilities.

**Complete step by step solution:**

When the null hypothesis $\left( {{H}_{0}}:\mu ={{\mu }_{0}} \right)$ is true and we reject it, we make a type 1 error. The probability of making a type I error is $\alpha $, which is the level of significance you set for your hypothesis test. An $\alpha $ of 0.05 indicates that we are willing to accept a 5% chance that we are wrong when you reject the null hypothesis.

When the null hypothesis is false and we fail to reject it, you make a type 2 error. The probability of making a type II error is $\beta $, which depends on the power of the test

The formulas for finding the probabilities are

Type 1: \[P\left( \text{rejecting }{{H}_{0}}|{{H}_{0}}\text{ true} \right)\] and Type 2: \[P\left( \text{accepting }{{H}_{0}}|{{H}_{0}}\text{ false} \right)\].

**Note:**

To lower this risk in type 1, we must use a lower value for $\alpha $. However, using a lower value for alpha means that we will be less likely to detect a true difference if one really exists. We can decrease your risk of committing a type 2 error by ensuring our test has enough power. We can do this by ensuring your sample size is large enough to detect a practical difference when one truly exists.

Recently Updated Pages

Cryolite and fluorspar are mixed with Al2O3 during class 11 chemistry CBSE

Select the smallest atom A F B Cl C Br D I class 11 chemistry CBSE

The best reagent to convert pent 3 en 2 ol and pent class 11 chemistry CBSE

Reverse process of sublimation is aFusion bCondensation class 11 chemistry CBSE

The best and latest technique for isolation purification class 11 chemistry CBSE

Hydrochloric acid is a Strong acid b Weak acid c Strong class 11 chemistry CBSE

Trending doubts

Give 10 examples for herbs , shrubs , climbers , creepers

Difference Between Plant Cell and Animal Cell

Write a letter to the principal requesting him to grant class 10 english CBSE

Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE

Fill the blanks with the suitable prepositions 1 The class 9 english CBSE

Name 10 Living and Non living things class 9 biology CBSE

Change the following sentences into negative and interrogative class 10 english CBSE

List some examples of Rabi and Kharif crops class 8 biology CBSE

Write the 6 fundamental rights of India and explain in detail