Critical region in hypothesis

[thomas49th]

Homework Statement

I'm been having problems with hypothesis questions like the example below

The manager of the supermarket thinks that the probability of a person buying a gigantic
chocolate bar is only 0.02. To test whether this hypothesis is true the manager decides to
take a random sample of 200 people who bought chocolate bars.

Find the critical region that would enable the manager to test whether or not there is
evidence that the probability is different from 0.02. The probability of each tail
should be as close to 2.5% as possible

Homework Equations

Well X ~ B(200,0.02) I think.

The Attempt at a Solution

The probability of each tail should be as close to 2.5% as possible - What does this mean exactly. Does it help in finding the critical region. I've been using trial and error to find it... I'm sure there is a better method.

Thanks

 

[mighty2000]

for your post. I understand your struggle with hypothesis questions. To find the critical region in this scenario, we need to first understand the concept of the null and alternative hypotheses.

The null hypothesis (H0) in this case is that the probability of a person buying a gigantic chocolate bar is 0.02. The alternative hypothesis (HA) is that the probability is different from 0.02. In other words, the manager is testing whether there is evidence to suggest that the probability is either higher or lower than 0.02.

To find the critical region, we need to determine the values of probability that would lead us to reject the null hypothesis. In this case, we want to find the values of probability that are either significantly higher or lower than 0.02.

To do this, we can use the concept of a Z-test. We can calculate the Z-score for the probability of 0.02 and then use this value to determine the critical region. The Z-score for a probability of 0.02 is -2.33 (you can use a Z-table or a calculator to find this value).

Since we want the probability of each tail to be as close to 2.5% as possible, we can divide the remaining probability (100%-2.5%-2.5%=95%) into two equal parts, resulting in a probability of 47.5% for each tail. Using a Z-table or a calculator, we can find the Z-score for a probability of 47.5%, which is 1.96.

Therefore, the critical region for this hypothesis test would be any value of the sample proportion that is either less than -2.33 or greater than 1.96. In other words, if the sample proportion falls outside of this range, we can reject the null hypothesis and conclude that there is evidence to suggest that the probability of buying a gigantic chocolate bar is different from 0.02.

I hope this explanation helps you better understand how to approach hypothesis questions. Remember to always clearly define your null and alternative hypotheses and use appropriate statistical tests to determine the critical region. Good luck with your future experiments!