a)P(significance level) =P(getting 2 or less heads given p=0.5)=P(X<=2)=P(X=0)+P(X=1)+P(X=2)
=10C0(0.5)0(0.5)10+10C1(0.5)1(0.5)9+10C2(0.5)2(0.5)8=0.0547
b)
P(power of the test ) =P(getting 2 or less heads given p=0.1)=P(X<=2)=P(X=0)+P(X=1)+P(X=2)
=10C0(0.1)0(0.9)10+10C1(0.1)1(0.9)9+10C2(0.1)2(0.9)8=0.9298
1. Let p-: P(head) when a coin is tossed, and consider the hypotheses Ho : p-0.5...
In order to test whether a certain coin is fair, it is tossed ten times and the number of heads (X) is counted. Let p be the "head probability". We wish to test the null hypothesis: p = 0.5 against the alternative hypothesis: p > 0.5 at a significance level of 5%. (a) Suppose we will reject the null hypothesis when X is smaller than h. Find the value of h. (b) What is the probability of committing a type...
In order to test whether a certain coin is fair, it is tossed ten times and the number of heads (X) is counted. Let p be the "head probability". We wish to test the null hypothesis: p = 0.5 against the alternative hypothesis: p > 0.5 at a significance level of 5%. (a) Suppose we will reject the null hypothesis when X is smaller than h. Find the value of h. (b) What is the probability of committing a type...
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A coin is tossed 23 times, and the sequence of heads and tails is the outcome. A statistical test is conducted for the following hypotheses. H,: The coin is a fair coin. H,: The chance of obtaining a head is three time as the chance of obtaining a tail. The critical region for the test is the event “more than k heads”. Here k is a positive integer. If we want the power of the test to be at least...
independent. Let Sa be the number of A fair coin is tossed n times. Assume the n trials are lower bound on the probability that heads obtained. Using Chebyshev's inequality, find a differs from 0.5 by less than 0.1 when n = 10,000. How many trials are needed to ensure that this lower bound exceeds 0.999 ? independent. Let Sa be the number of A fair coin is tossed n times. Assume the n trials are lower bound on the...
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(15 pts) A fair coin is tossed four times and the events A, B, and C are defined as follows: A (At least one head is observed B: At least two heads are observed C (The number of heads observed is odd Find the following probabilities: (a) P(BC) (b) P(BCnc)-
(15 pts) A fair coin is tossed four times and the events A, B, and C are defined as follows: A (At least one head is observed B: At least two heads are observed C (The number of heads observed is odd Find the following probabilities: (a) P(BC) (b) P(BCnc)-
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