9.43 Is the die fair? You suspect that a die has been...

9.43 Is the die fair? You suspect that a die has been altered so that the outcomes of a roll, the numbers 1 to 6, are not equally likely. You toss the die 600 times and obtain the following results: Outcome 1 2 3 4 5 6 Count 87 80 125 117 100 91 following results Perform a chi-square goodness of fit test, to teach whether each face is equally likely. Make sure to include the hypothesis, test statistic, p-value, and conclusion.

Transcript

00:02 In the asked question, we suspect that a die has been altered so that the outcomes overall the numbers from 1 to 6 are not equally likely therefore we test the die 600 times and obtain the given results we have the outcome might be 1 2 3 4 5 or 6 and the count for each one it's 87 80 120 117 -191 it's required to perform a kai -square goodness of bed test to see whether each phase is equally likely or not the first step is to include the hypothesis or state the hypothesis the null and the alternate one the null hypothesis here node will be the distribution p is equal to p node where p node is just 1 over 6 this if it was fair and h1 1 over 6 it's not 1 over 6 it's 1 over 6 and 1 over 6 and so on 1 over 6 1 over 6 1 over 6 and so on 1 over 6 1 over 6 1 over 6 1 over 6 and 1 over 6 you have 1 over 6 6 times and h1 will be b is not equal to b node this is the first step the second step is to calculate the test statistic the statistic here is k squared which equals n divided by b squared will be here is 1 over 6 multiplied by the sum of b i minus b i node squared from i equals 1 to 6 because we have here 6 categories what is pi sorry this is b i hat what is b i had it's the numbers we've got from our experiment from our test then here we should get b had it's 87 divided by 600 which is 29 divided by 200 then it's 80 divided by 600 2 divided by 15 and so on it's 5 divided by 24 it is 39 divided by 200 it's 1 over 6 and finally it's just 91 divided by 600 now now we can calculate the test statistic.

03:52 It equals in the number of trials, we have conducted 600 trials divided by p squared, which is 1 over 6.

04:07 This is b node, which is 1 over 6 squared, multiplied by this sum squared, the sum of the difference is square.

04:25 The first one will be 29 divided by 2.

04:29 200 minus 1 over 6 squared plus the second 1 divided by 15 minus 1 over 6 square plus 5 divided by 24 minus 1 over 6 squared plus 39 divided by 200 minus 1 over 6 squared plus 1 over 6 squared is 0 finally 91 divided by 600 minus 1 over 6 squared is 0 finally 91 divided by 600 minus 1 over 6 squared is 0 finally 91 divided by 600 minus 1 over 6 squared these are the six terms then the kai square equals 93 .84 this is the second step what is the third step is to calculate the b value the b value is calculated using the level using the kai square value here it is the probability of the kai square value here it is the probability of the k k squared to be greater than 93 .84.

05:55 And what is the number of degrees of freedom for this kai squared test? it is the number of categories minus 1...

Question

Please give Ace some feedback