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Hello everyone.
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So in this question we have given this grades, a is 25%, b is 25%, c is 40%, d is 5 % and f is 5%.
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Now at the end of a randomly selected semester, the following number of grades were recorded and this is the data.
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Now we need to find kai square test statistic to determine if the grade distribution is different than expected.
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So now first of all, we will write our hypothesis.
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So here, null hypothesis is the district.
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Of grade, the distribution of grade, the distribution of grade is same, is same as expected, whereas our alternative hypothesis is the opposite of the null hypothesis.
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So the alternative hypothesis is the distribution of grade, the distribution of grade is different than expected.
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So these are our hypothesis.
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Now we will find the total number of number which is n is equal to 36 plus 42 plus 60 plus 8 plus 14.
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Now on adding we will get equal to 160.
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Now we will make one calculation table where in the first column we will write grades.
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Then in the second column we will write probability of success of each grades.
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Then observed frequency of each grades.
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Then expected value of each grade.
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And we can find this by multiplying n with p.
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And at last we have one column where we will calculate.
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Observed minus expected value square divided by expected value.
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So our grades are a, b, c, d and f.
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And probability of success of each grade, that is for grade a is 0 .25.
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For grade b, it is also 0 .25.
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For grade c, it is 0 .40.
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For grade d, it is 0 .05...