In Exercises 33–40, use the given probability value to determi...

Question

In Exercises 33–40, use the given probability value to determine whether the sample results are significant.

Voting Repeat Exercise 33 after replacing 40 Democrats being placed on the first line of voting ballots with 27 Democrats being placed on the first line. The probability of getting a result as high as 27 is 0.029792.

Accepted Answer

Hello there. Today we're gonna solve the following practice problem together. So first off, let us read the problem and highlight all the key pieces of information that we need to use in order to solve this problem, determining whether the sample results are significant. A recruitment officer was supposed to use a random process to assign the order in which applicants were called for interviews. Among 41 different sessions, female applicants were placed in the first interview slot 27 times. The probability of getting a result high or higher by random chance is 0.031728. Assuming the process was truly random, is the result of 27 female names being listed first significantly low, significantly high, or neither? Awesome. So it appears for this particular problem, we're ultimately trying to say, or are ultimately trying to solve for. We're trying to determine whether or not, assuming that this process was truly random, is the result of 27 female names being listed first, considered either significantly low, significantly high, or neither as an answer. So with that in mind, let's read off our multiple choice answers to see what our final answer might be. A is neither significantly low nor high. B is significantly high. C is significantly low, and D is cannot be determined. Awesome. So, first off, what we need to do in order to solve this problem is we need to understand the probability context. So the context of our probability that we're trying to examine. So, with that said, we need to note once again that we are told that the female applicants were placed in first. Slots, or rather it was they were placed in the first interview slot 27 times. Out of the 41 total sessions. So that's important to note. And with that in mind, we need to note that because they were placed first in 27 out of 41 sessions, and we also need to note that the probability of this happening randomly will be what we'll call P, the probability and the probability P, is going to be equal to, as we're told by the problem itself, 0.031728. Fantastic. So now, our second step is we need to recall and use the rule for significance. So as we should recall and note, a result is considered statistically significant if the P value is less than or equal to 0.05. So that will mean that 0.031728 is less than 0.05. So therefore, as a result, the outcome is significantly statistically significant. So once again, because 0.031728 is less than 0.05, that means that our outcome for this particular problem is statistically significant. So that will mean for our 3rd step, we need to determine the direction of the significance. And as we should recall a note, since the number of females in the first slot or specifically the first interview slot is higher than expected. That will mean that the probability of that happening by chance is low, so that will mean that the result is significantly high. So that will mean that our final answer, without a doubt has to be multiple choice answer letter B, which is significantly high. And that's it. That is our final answer. Thank you so much for watching. Hopefully that helped, and I can't wait to see you in the next video. Bye.

��app

Key Concepts

Significance Level

P-value

Hypothesis Testing

Watch next