Q4. I’m going to share a real-life personal experience for this question: I may
ID: 3233795 • Letter: Q
Question
Q4. I’m going to share a real-life personal experience for this question:
I may not be the best cook in the world, but I have never started a fire while cooking. Despite this, my smoke alarm frequently goes off when I’m cooking. Obviously, the smoke alarm is making an error.
a) What Type of error is my smoke alarm making?
Explain your answer, making sure to include appropriate Ho and Ha statements as well as definitions for different types of hypothesis testing errors.
b) As some of you may be able to relate to, it is very annoying when the smoke alarm goes off even when there is no fire. I have to climb up there, fan it or remove the battery, etc. When this happens, I am tempted to write a letter to the smoke alarm company asking them to change the level setting on the smoke alarms they make so they wouldn’t go off by mistake so often. What would I be asking the company to do with the size of , make it bigger or make it smaller?
Explain your answer.
c) Why don’t I write that letter? Yes, laziness may have something to do with it, but I’m looking for an important statistical answer.
Q4. I’m going to share a real-life personal experience for this question:
I may not be the best cook in the world, but I have never started a fire while cooking. Despite this, my smoke alarm frequently goes off when I’m cooking. Obviously, the smoke alarm is making an error.
a) What Type of error is my smoke alarm making?
Explain your answer, making sure to include appropriate Ho and Ha statements as well as definitions for different types of hypothesis testing errors.
b) As some of you may be able to relate to, it is very annoying when the smoke alarm goes off even when there is no fire. I have to climb up there, fan it or remove the battery, etc. When this happens, I am tempted to write a letter to the smoke alarm company asking them to change the level setting on the smoke alarms they make so they wouldn’t go off by mistake so often. What would I be asking the company to do with the size of , make it bigger or make it smaller?
Explain your answer.
c) Why don’t I write that letter? Yes, laziness may have something to do with it, but I’m looking for an important statistical answer.
Explanation / Answer
a)
Ho = Smoke alarm rings when there is fore
Ha = Smoke alarm rings even when there is no fire
Here the the error is the type 1 error.
A type I error is the incorrect rejection of a true null hypothesis i.e a type I error is detecting an effect that is not present.
b)
Here we should decrease the level of significance (alpha) as it decrease probability of Type 1 error .
The level of significance, alpha, is defined as the probability of a Type I error. The researcher picks this value as their threshold– the maximum acceptable probability of making a Type I error. The lower alpha is, the harder it is to reject the null hypothesis
c)
We should not be writing the letter as the decrease in the level of significance - decrease probability of Type 1 error but increases probability of type 2 error.
So we can be in the danger of alarm not ringing even in the case of a fire.
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