4. (2.5 points (5*0.5)) We assigned 80 individuals to a...

4. (2.5 points (5*0.5)) We assigned 80 individuals to a certain class based on their numbers of hours they regularly do sports a week. Afterwards, we asked them if they feel down or balanced, in other words, if they belong to class \"I\" (Null) or class \"II\" (Non-null). We obtained the confusion matrix: \begin{tabular}{|c|c|c|c|} \hline Predicted \\ True & I & II & Total \\ \hline I & 35 & 8 & 43 \\ \hline II & 3 & 34 & 37 \\ \hline Total & 38 & 42 & 80 \\ \hline \end{tabular} Calculate the accuracy, the false positive rate, the true positive rate, the positive predictive value and the negative predictive value.

Transcript

00:01 So our question says ecem claims that the main tmn 168 score attained by psychology students is actually equal to 40.

00:07 Cedar suspects that the mean score is different from what acem claimed and is select a random sample of 81 psychology students.

00:14 The mean of the sample is actually 43 .4 and the population standard division is measured to be 9 .3.

00:22 So we have series of questions to work on.

00:24 So let's extract out all of our details first.

00:27 So we have a population mean new to be equals to 40 we have our sample size n to be cost to 81 we have the sample mean to be cost to 4 to 3 .3 and we have the population standard division to have a value of 9 .3 so the first question says states the null and alternative hypothesis so let's take a closer look at the question again so ecm claims that the mean scm and 16 is called at by psychology student is 40 so cedar suspects that the mean score is different from is different from one e cm claim you didn't say it is more or less it is different so that means our null hypothesis h not is based on the fact that mu is equal to 40 and the alternative hypothesis is based on the fact that mu is not equals to 40 so the next question uh says that um is this a two -sided test or not so as you can see from our alternative we can see that our tests here includes the not equality sign which is a sign for a two -tailed test so yes our test is actually a two -sided test the next question is so we are supposed to i perform our hypothesis test and then sorry get our test statistics and check ecm's claim the same scheme so to take its same claim we need to get our test statistics really to state our decision rule so i will start by stating the decision rule.

02:07 So for my decision rule, i have that if the p -value is greater than alpha, we actually fail to reject the null hypothesis.

02:18 And if our p -value is lesser than alpha, we actually reject the null hypothesis.

02:24 Our alpha level is according to our question.

02:26 We have our alpha level to be 0 .05.

02:31 So let's get our test statistics.

02:33 Because before you can be able to test e cem's claims we need to get the decision rule on our test statistics so we have the value of the population standard deviation our sample size is greater than 30 so that means our test statistics is going to be a z test so we have that z is equal to xx minus mil divided by z divided by the square root of n so our x by in this case is 43 .3 minus 40 divided by our zima is 9 .3 divided square root of 81.

03:06 So we have our z is equal to.

03:09 So let's use our calculator to work on this.

03:14 So for 3 .3 minus 40.

03:16 We have our answer to be 3 .3 divided by so 9 .3 divided by square root of 81...

Question

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