Let X denote the number of heads that appear when five coins are tossed. It is c
ID: 3226147 • Letter: L
Question
Let X denote the number of heads that appear when five coins are tossed. It is clear that X has binomial distribution with p_k = P(X = k) = n!/l!(n - k)! p^k (1 - p)^n - k for k = 1, 2, 3, 4, 5. The following data recorded the frequency distribution of the number of heads in n = 40 tosses of the five coins. The null hypothesis is that the observations follow are consistent with the binomial distribution with p = 1/2. a) Compute the expected cell frequencies and fill in the table. b) After combining cells with small expected frequencies, compute the chi^2 statistic and compute the number of degrees of freedom. c) Use the value of chi^2 obtained in part (b) to test H_0 at the 5 percent level of significance.Explanation / Answer
df = number of rows -1 = 5
Test statistic = 19.6
X2 critical at 5% = 11.1
since TS< X2 critical
we can not reject te null hypothesis.
O p Ei (npi) (Oi-Ei)^2/Ei 1 0.03125 1.25 0.05 17 0.15625 6.25 18.49 15 0.3125 12.5 0.5 10 0.3125 12.5 0.5 6 0.15625 6.25 0.01 1 0.03125 1.25 0.05 1 19.6Related Questions
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