A color code personality test categorizes people into four...

A color code personality test categorizes people into four colors – Red (Power), Blue (Intimacy), Green (Peace), and Yellow (Fun). In general, 25% of people are Red, 35% Blue, 20% Green, and 20% Yellow. An art class of 45 students is tested at a university and 7 are found to be Red, 18 Blue, 9 Green, and 11 Yellow. Can it be concluded that personality type has an impact on students’ areas of interest and talents, such as artistic students and state the p-value? Test at a 0.05 level of significance. Red Blue Green Yellow Observed Counts 7 18 9 11 Expected Counts 11.25 15.75 9 9 A. Yes, the p-value = 0.501025 B. No, the p-value = 0.501025 C. No, the p-value = 0.498975 D. Yes, the p-value = 0.498975

Transcript

00:01 I mean, this question basically look at the, how to say the color code personality.

00:09 So let's look at four colors, right? one is right, i call it just an arrow, and blue and a green and a yellow, right? and it turns out that you have a number of students, right? the observed cons of all these different colors actually is they observed, right? they observed the count for the color, so actually 7, 18, 9, 11, right? but the expected counts for this should be actually 11 .25, 15 .7599, right? so that would be the expected cons.

00:46 So actually you ask you to basically find the task of test, right? and found, of course, the p value.

00:56 That's what you asked to do, right? so basically you need to calculate that, of course, the cut square test value for this, which is given by, you know, you just take the observer value minus the corresponding expected value and square them and divided by the expected value and the sum overall of these values, right? so you'll find this, for example, the first one you get a 7 minus 11 .25 and squared and divided by 11 .25, right? and plus all the same, all similar values for different pairs, right? for the pairs, right? so you get 11 minus 9 squared and divided by 9, right? now you do the calculation, you would have found this actually to be given by 4 .25 squared divided by 11 .25 plus 2 .25 squared divided by 5 .25 divided by 15 .75 plus 0 plus 4 divided by 9.

01:59 And i found that to be given by 2 .3 7, right? so that's my k square test.

02:05 So what would be the p value? but the p value actually you can find from the k square table.

02:12 So basically you set the ksquare score to be 2 .3 at the p value, right? so this is the p value.

02:20 And degree freedom is given by, you know, the product of the number of columns, which is you have four columns minus one.

02:27 So it's three times the number of rows minus one.

02:30 So you have two rows, minus one, right? three times one, so that's three, right? so that's degree freedom, which is three.

02:35 And you say this to be 2 .37...

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