Question

What is a null hypothesis and what is an alternative hypothesis? How do you choose the null hypothesis in general? Give an example What is type I error? What is type II error? What is the significance level? What is the power of the test? What is the p-value of a hypothesis test?.

Please type the answer as I have difficulties understanding handwritten answers. Thanks

Answer 1

Answer:-

Null Hypothesis:-

                It is the boring hypothesis which claims that things are "just fine" or "expected". It is denoted by "H_o".

Ex:- "Machine is working just fine". If the machine mean output is supposed to be 5 then, in symbols,

        we write: H_o : =5.

Alternative Hypothesis:-

             It states a claim against null. It is denoted by H_A or H₁. It always contains te strict inequality sign,

i.e., <, >, or

Here, Null hypothesis has sign of equality i.e., . Some authors prefer using "=" in all 3 cases of null hypothesis. The Alternative hypothesis determine the direction of Hypothesis, "<" means left tailed, ">" right tailed, and means two tailed hypothesis.

Type I error:-

               It is the probability of rejecting the null hypothesis when the null hypothesis is correct.

Type II error:-

              It is the probability of accepting the null hypothesis when the null hypothesis is incorrect.

Ex:-

If from a populations of apples a sample is taken and based on that sample we decide that the apples are not of good quality, but actually the apples are of good quality, we have committed Type I error

While as based on the sample we decide that the apples are of good quality but actually they are not then we have made Type II error.

Hence, Type I error is also called as Producer's risk whereas Type II error is also called as Consumer's risk.

Ex:- "The machine is overfilling". In symbols, we write: H_A : > 5