Question
(A) Suppose that the probability of cure (success) is theta when a certain medicine is used to treat a particular disease. We wish to test H_0: theta = 0.8 against H_1: theta = 0.4. The test statistic is X, the number of cures in 5 trials, and H_0 is to be accepted if x greaterthanorequalto 3 (otherwise H_0 is to be rejected). Find the significance level alpha (probability of type l error) and beta, the probability of type II error. (B) Suppose a random sample of size n = 5 from a continuous distribution has sample mean x = 6.1 and sample standard deviations s = 8.2. Let mu be the population mean. Test H_0: mu = 5 against H_1: mu > 5 at alpha infinity 5% level of significance. (C) The data below is the "ability in Mathematics" and "interest in Statistics" for a random sample of students of Kuwait University. Test at 0.05 level of significance whether a person's ability in Mathematics is independent of his or her interest in Statistics.
Explanation / Answer
b) TS = (xbar - mu)/(s/sqrt(n))
= (6.1 - 5)/ ( 8.2 /sqrt(5))
= 0.2999603
this is t- distribution with df = n-1 = 4
t-critical = 2.132
since TS< critical value , we fail to reject the null
c)
TS = 64.2797
this is chi-square distribution
df = (r-1)(c-1) = 4
critical value =
since TS >critical value , we reject the null hypothesis and conclude that there is significant evidence that both are dependent
Post a) part again.
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c1 c2 c3 sum r1 126 84 30 240 r2 116 122 62 300 r3 28 94 58 180 sum 270 300 150 720 Eij 1 2 3 expected 1 90 100 50 2 112.5 125 62.5 3 67.5 75 37.5 0i 126 84 30 116 122 62 28 94 58 Ei 90 100 50 112.5 125 62.5 67.5 75 37.5 (Oi-Ei)^2/Ei 14.4 2.56 8 0.108889 0.072 0.004 23.11481 4.813333 11.20667 sum 64.2797
