Two classes take an exam. We have five scores from the first class and 4 from th

Question

Two classes take an exam. We have five scores from the first class and 4 from the second. We are interested to see if there is a difference between the median return of the two groups. a) Find the test statistic for the appropriate hypothesis test. b) Suppose the test statistic is +/- 1.645. Can the null hypothesis be rejected? Why or why not? In a recent election, a sequence of votes showed H H H T T H H T T T T H H H H T T T T T. We wish to test this sequence for randomness, so a two-tailed one sample runs test is to be performed. a. If mu_R = 10.9 and sigma_R = 2.15, find the test statistic. b. Find the critical value(s) for alpha = 0.05.

Explanation / Answer

H0: 1 - 2 = 0 i.e. (1 = 2)

H1: 1 - 2 0 i.e. (1 2)

S2p= (n1-1)S21+(n2-1) S22/(n1-1) +(n2-1)

      = (5-1)*(33.61547)^2+(4-1)*(44.34712)^2/(5-1)+(4-1)

      = 4520+5900/7

      =1488.57

t=(X1-X2)-(µ1- µ2)/ S2p(1/n1+1/n2)

t=(94-65)-0/1488.57(1/5+1/4)

t=29/25.88

t=1.12

tCRICT is +-1.645 and hence cannot reject null hypothesis.

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