# MATHS – SHORT RESPONSES

PART I: SHORT RESPONSEDirections: Please answer each of the following questions thoroughly.1. What is one-way analysis of variance used for? What are the requirements for one-way analysis of variance?2. What is two-way analysis of variance used for? What are the requirements for two-way analysis of variance?3. What is the main difference between one-way analysis of variance and two-way analysis of variance?4. In one-way analysis of variance tests, do larger test statistics result in larger P-values, smaller P-values, or P-values that are unrelated to the value of the test statistic?5. What are the advantages and disadvantages of nonparametric tests?6. Why is the sign test considered to be a “nonparametric” test of a “distribution-free” test?7. Assume that matched pairs of data result in the given number of signs when the value of the second variable is subtracted from the corresponding value of the first variable. Use the sign test with a 0.05 significance level to test the null hypothesis of no difference.Positive signs: 13; negative signs: 1; ties: 0 (from a preliminary test of the MicroSort method of gender selection)Positive signs: 5; negative signs: 7; ties: 1 (from a class project testing for the difference between reported and measured heights of males)8. In a study of fraternal twins of different genders, researchers measured the heights of each twin. The data show that for each matched pair, the height of the male is greater than the height of his twin sister. What is the value of T?9. Listed below are the genders of the first 25 subjects listed in Data Set 3 in Appendix B. Use that sequence to identify the values of n1, n2, and G that would be used in the runs test for randomness. M M M M M M M M M M M M M M M M M M F F M F M M M10. A New York Times article about the calculation of decimal places of noted that âmathematicians are pretty sure that the digits of are indistinguishable from any random sequence.â Given below are the first 30 decimal places of ?. Test for randomness of odd (O) and even (E) digits. 1 4 1 5 9 2 6 5 3 5 8 9 7 9 3 2 3 8 4 6 2 6 4 3 3 8 3 2 7 9

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