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Ashely S.

Intro Stats / AP Statistics

7 months, 1 week ago

Questions have been provided. The data that shows the Asian favorite type of music of 1779 randomly selected people. And the tests. The attorney had been asked to test the claim that the Agent preferred music type are independent. And here I'm prize given to me 0.05. But that is the level of significance. Right now. Here we have to first formulate the null hypothesis and we alternate hypothesis for this. So the null hypothesis would be that two category girl, Betty booze, that is the music deep and each are independent. Right? And the alternative hypothesis would be that new big type and age dependent With the level of significance of 0.05. Now, first of all, we have to calculate the test statistic for the expected values. Okay right. So here we will add one more column that is we have to totally ah the all all of the values here. So The total of these four types of movies is will be 189. And the four of this will be 213 then therefore be 200. And the total of this will be 1778. And we had one rubio That tells the total of the role and total of the column. So here is really to 1,4, 1 86 and 188 and 191. And the total year it should be 7 79. Because the total of the uh total of people that have been selected at 779. Right? So, so here we need all right. They expected values. That is easy equal to the total of the rules, multiplied by the total of the columns Undivided weather total number of the data which we have been used. So it will be 189 and 2 214. And multiply 779. That will be 51.92. So that's how we calculate the expected values. Right. So fantastic. Only the deputy will that is 1st column will be the observed value. Then we calculate the expected value of each. Then the difference between the two, then the square of this. So this is basically the Javier performing here. They start to still want the high square analysis and the guy square will be here squares divided way expected value. That is right. So First we have is 21 observed value. And for that the expected value is 51.92 and all minus e will be minus 50.92. six point of view Seven than it will be 18.41. Right, next is 45. So it will be 45.13 -0.13 0.02 zero. Next to your value is 90. That comes to be 45.61, 24.39197, and 53.20. And the next it will come three that is 4 to 6.34 13.3 Schools .963 .84. And we have to calculate this for all the values that have been of the right 9.49 89.99, 1.54. When Guns 55, 2.86, 400.85 1234. That makes use for two 48 65. Mm hmm 47. Let's calculate here. 1st For 42. It will be 51 points. Oh, you I left 9.40 to 8.44, 22, 2 to 17.85 and 0.344 65. Which will be 54.9 for 10.6101 point 1691 point eight and 4 for this, 24 to 7.75 -2.75 0.57101. So that becomes the next value. 31, two servants the 39, and 53. So these are the values that we need to calculate for going to seven, 1917.27, and 6.18. Yes, 3 49.04, 7.96, 1 and 1.29 48.6 to 11.3 to 1, 29.42 and 2.66. And then next 34 39 it will be 42.26 .72 and 43.40, one of 3.26 -17.7- 9.60. and for reality, TV 10.6431, 3 Point 8792.20. Then we're going to 57.35 and 2.12. And finally to the total of these older I squared value that come and it will come out to be 91.10 here. Right? So the test statistic that this guy's graduate, just some of the Divided by, even though it comes out to be 91.10 now and they use might as well to our minus one and two c minus one. So we have these four minus one Is 4 -1. That comes out to be nine and alpha here is 0.05. So the critical value the critical Well you will be equal to 16.9189. Now the Chi Square started sticks Is equal to 91.10. It is a critical value here is 16.91 right through this is a critical value. So what we will do here, we have to reject the none hypothesis At alpha is equal to 0.05. So there is a sufficient evidence concluding that music type is dependent on the age. This is the answer for the given question will decide to thank you for watching.

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