Evaluate whether each of the following is true or false. Circle the number besid

Question

Evaluate whether each of the following is true or false. Circle the number beside the statement if it is true. Toss a fair coin twice, and let X be the number of times head comes up. the expected value of X_i X Sample means. denoted as is a random variable whose mean is equal to zero. X is a random variable with mean equal to mu, standard deviation is sigma. Let Z = X - mu/sigma + Then the expected value of Z is 2, the variance of Z is 1. Sample standard deviation, denoted as S; is a random variable. The significance level of a test is the probability that the null hypothesis is false. The power of a test is the probability of accepting a null hypothesis that is true. If a null hypothesis is rejected against an alternative at the 5% level, then using the same data, it must be rejected against alternative at the 1 % level. The p-value of a test is the probability that the null hypothesis is true. According to Chebyshev's Theorem, no matter how a random variable is distributed, at least 2/3 of the observations of a random variable lie within plusminus 3 standard deviations of the mean. 10. X1 and X2 are both random variables with same probability distribution, then X1 -X2 = 0

Explanation / Answer

1) false

2)false

3)false ; expected value=0

4)true

5)false

6) false

7)false

8)true

9)true

10)False

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