A Write out the null and alternative hypothesis that are used in chi-squared hyp
ID: 3363551 • Letter: A
Question
A Write out the null and alternative hypothesis that are used in chi-squared hypothesis tests. Do these null and alternative forms ever vary (i.e. are there different forms of the alternative hypothesis depending on whether or not the test is one-sided or two-sided? b. In a situation where the observed counts are exactly equal to the expected counts, what is the value of Chi-Squared? Are you likely to reject or accept Ho in that situation? c. In a situation where the observed counts are very different (either much bigger or much smaller) from the expected counts, are you likely to reject or accept Ho? Justify your answer.Explanation / Answer
A. Chi-squared goodness of fit test can be used to test whether the observations are arising out from a given distribution or not. The hypothesis can be like:
X1, X2, . . . , Xn iid sample. H0: X's ~ Poisson(p) vs H1: H0 is false there is a significant difference between the observed and the expected value.
No the alternatives doesn't change
B. No. When expected frequency and observed are exactly equal, the test statistics takes value 0. In this case, we can't reject null at any significance level as there is no strong evidence of significant difference. The chi-sq is a non-neg random variable, so the critical region got to be positive for any level of significance.
C. When the difference is large between observed and expected, the hypothesis is likely to be rejected as the value of (Oi-Ei)^2 will be large and we reject H0 in favor of alternative when the value statistic is larger than the critical value.
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