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Numerade Educator

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Problem 40 Hard Difficulty

Use the following information to answer the next three exercises. Suppose a group is interested in determining whetherteenagers obtain their drivers licenses at approximately the sameaverage age across the country. Suppose that the following
data are randomly collected from five teenagers in each region of the country. The numbers represent the age at which teenagers obtained their drivers licenses.
TABLE CANNOT COPY.
Enter the data into your calculator or computer.

p-value = ______

Answer

0.017

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Video Transcript

So, um, burgers question the first start to answer what is our DF the waiter in what is our d of denominator? So do you have no Warriner is, um K minus one k is a total a number of different group. In this case, we have five. So therefore our DF numerator is five minutes oneness four for our d of denominator, we have in total 20 values minus que, which is a total number of different group. So and minus K equals to 20 minus five different group equal suphan team. So thanks. We would fine. What is our s one? As to us three s for s five. So as one s two s three s words, five, they are the sun of each column. So s one mean it would be equals to 65.3 us too close to 66 as three equals 21075 point 84. As for equals Oh, sorry. So este is equals to 65.6. That's why I was like, Why the numbers so big s floor is equals to 65.7 as five equals to 67.7. Okay, So now, in order for us to calculate the p value, we have to know our what is our f statistic? Iss. So to tackle it F statistic, um, we would talk, really the mean square off between and means square off within. So for calculating means square between it would follow following formula. So the total cell Oh, me. So the total son of S J Square over NJ NJ is the number off value, Procol over the total. It's off us, jay, that some would be square and over and so to write, it s in terms of s one to s five. We would have as one square over in our case over four plus as two square over four plus dr dot to s five square over four blindness as one plus as two plus dot dot dot to s five that some would then square over the total value. The total elements in the data is 20. So we know that, um, the calculations you can do it yourself by plucky as one in this equation. And then the final answer would be 0.90 30. So to calculate, do this is not unless this is, um cell square value. And now we need Now we cook late Bean Square, So means square would be as us over, uh, K minus one. So in our case is DF numerator. It would be serial 0.90 3/4. Our final answer would be equal to zero point to to six. This is a mess between, so we know that I'm as between equals this value. Now we gonna find m s within. So m s within with B equals to us as within over de of denominator. In our case, this 15 So for s s with then equals to us as total minus s s between. So, for us as total has the following equation the total value um, you're X square liners some off all of your ex and then squaring that some over. And so in our case, the S s total would be equals two 1.7055 So now to calculate s with and we take s total minus as a Z, um, that s total minus as as between. So our final answer in this case would be our case would be 1.4795 But so now when we know our value for, uh, sorry. I made a mistake here. So this is This is a mess, Not s. So our s s value iss a Neary. Right? This hour s value is 0.903 My bet, And this would give us the result, um, of esto, as that's what then it was zero point. Hey, zero to 25 And after calculating as as But then we can now confidently calculate the f statistic f statistic. We'll wait s s within and then calculate m s within. So Emma's within would be as s over. The DF denominator is 15. You would have 0.80 to 5 over 15. This would be equals two zero point 05 Thief. To calculate the f statistic, it would be equal to MLS between over s within. So m s between equals two. Um, let's just grow up. And this between equals zero boy to to six over, um, as within 0.535 It give us an approximate numbers off. Four. Wait, Teoh One or 2.4 point two to just Let's just round it up. Okay? So now we have the F statistic. Um, we calculate the P value in which f, um, for 50 a mess for 15 larger than four point to to now wait can use any, like software or online calculator. This would give us the results of 0.17