In studying the occurence of genetic characteristics, the following sample data

Question

In studying the occurence of genetic characteristics, the following sample data were obtained. At the 0.05 significance level, test the claim that the characteristics occur with the same frequency. Use the table data to answer questions 1-4. Characteristics A B C D E F Frequency 28 30 45 48 38 39. Please show all your work and make sure the correct answer choice is clearly selected by the corresponding letter value listed in each question.

#1: The correct statement for the claim is: A) H1: The characteristics occur with different frequencies B) H1: The characteristics occur with the same frequency C) Ho: The characteristics occur with the same frequency D) Ho: The characteristics occur with different frequencies

#2: Critical Value is: A) 7.815 B) 11.071 C) 9.488 D) 4.605

#3: Test Statistic is: A) 15.177 B) 2.641 C) 10.531 D) 8.263

#4: Correct Conclusion is: A) Reject Ho which says there is sufficient evidence to support the claim of equal frequencies B) Fail to reject Ho which says there is insufficient evidence to warrant rejection of the claim of equal frequencies C) Fail to reject Ho which says there is sufficient evidence to support the claim of equal frequencies D) Reject Ho which say there is sufficient evidence to warrant rejection of the claim of equal frequencies

Explanation / Answer

here we go for chi-square test for goodness of fit

and chi-square= sum(O-E)2/E with k-1 df, where k is number of class

answer of 1)C) Ho: The characteristics occur with the same frequency and

  A) H1: The characteristics occur with different frequencies

answer of 2)Critical Value is:B) 11.071

answer of 3)Test Statistic is: D) 8.263

answer of 4) as the test statistic 8.263 is less than the critical value 11.071 so answer is

D) Reject Ho which say there is sufficient evidence to warrant rejection of the claim of equal frequencies

A B C D E F Total observed(O) 28 30 45 48 38 39 228 Expected(E) 38 38 38 38 38 38 228 O-E -10 -8 7 10 0 1 (O-E)2 100 64 49 100 0 1 (O-E)2/E 2.631579 1.684211 1.289474 2.631579 0 0.026316 8.263158 chi-sq(.05,5)= 11.0705 Test statistic= 8.263

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