Question

Give an example of a hypothesis test in which the significance level should be very small and one that is not as strict.

Explain the errors that could be made based on these levels.

Answer 1

Lower significance levels indicate that you require stronger evidence before you will reject the null hypothesis.

For example, a physicist wants to test his new equipment used measure small measurements against his old equipment. For him the measurement should be precise upto nanometers. So, in this case he will form a hypothesis test with very low level of significance.

A Type I error is when we reject the null hypothesis when it is true. The symbol α (alpha) is used to represent Type I errors. This is the same alpha we use as the level of significance. By setting alpha as low as reasonably possible, we try to control the Type I error through the level of significance.

A Type II error is when we fail to reject the null hypothesis when it is false. The symbol β (beta) is used to represent Type II errors.

Type I error occurs when a researcher incorrectly rejects a true null hypothesis. This means that your report that your findings are significant when in fact they have occurred by chance.

Type II error occurs when a researcher fails to reject a null hypothesis which is really false. Here a researcher concludes there is not a significant effect, when actually there really is.