Question

I have calculated a probability of type two error at alpha 0.1 as 0.05730834612602564 and 0.05 as 0.11282997108101914. From these values how would i conclude the sampling method is good enough to reduce the effort(in my problem statement)

How should i interpret the value of chi square test, where the result is

statistic=15.066337549525954, pvalue=0.019746985983350823

Answer 1

obs	type-1 error	type-2 error
1	0.1	0.05730834612602564
2	0.05	0.11282997108101914

Type 1 error is rejecting the null hypothesis even when its true.

Type 2 error is accpeting the null hypothesis when it is false.

It can be observed that in observation 2 the sum of both type 1 and type 2 error is less compared to the sum of type 1 and type 2 error in observation 1.

So, ideally observation 1 is a better choice because sum of errors is low in that case.

But finally it depends on what kind of experiment is done, eg in medical cases is null hypothesis is patient is suffering from a disease and alternate is he is not suffering from a disease so is type 1 error is high even if he is suffering from a disease because of high type 1 error we mat reject Ho and hence it would create problems for the patient.

The value of Chi-square statistic is

statistic=15.066337549525954

pvalue=0.019746985983350823

So, depending on my probability of type-1 error i can arrive at conclusions.

1) If type-1 error is 5% that is alpha=0.05 then as pvalue is less than 0.05 then we reject the null hypothesis.

2) If type-1 error is 10% that is alpha=0.1 then as pvalue is less than 0.05 then we reject the null hypothesis.

3) if type-1 error is 1% that is alpha=0.01 then as pvalue is greater than 0.01 then we accpet the null hypothesis.