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SP06A_EC41_F09

# SP06A_EC41_F09 - EC 41 UCLA Sample Problems#6A Sections 6.3...

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EC 41; UCLA; Sample Problems #6A Sections 6.3 and 6.4, (and geometric distribution from 5.2) revised - numbering and typo for #12 fixed 1) Suppose someone is convicted of a crime if their guilt is “beyond a shadow of a doubt” = when there is only a 1% chance they are truly not a criminal. a) If convicting a true non-criminal is Type I error, what is Type II error? b) What corresponds to the “power” of a test in this setting? c) How could the power be increased in this setting? 2) You must decide which of two possible distributions a random variable X has, p 0 or p 1 . The probabilities for specific values of X are: x 0 1 2 3 4 p 0 .05 .05 .1 .2 .6 - The Null Hypothesis is: H 0 : p 0 is correct p 1 .2 .2 .2 .2 .2 - The Alternate Hypothesis is: H A : p 1 is correct Suppose you follow the rule: accept H 0 if X = 3 or 4 and reject H 0 otherwise a) What is the probability of Type I error? b) What is the probability of Type II error? c) What is the power of this testing procedure? 3) You think wages for a group of workers are less than \$10 per hour and would like to find evidence to support this claim. You assume it is impossible for wages of this group to be more than \$10, so you use a one-tail test. Choose a 5% level of significance, so the one-tail Z-critical will be -1.645. The true standard deviation of wages in this population is \$8 per hour. Consider the sample mean from a sample of 16 workers. Assume we can treat it as a simple random sample (SRS). Consider a specific alternative value for the true sample mean = \$6 per hour.

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SP06A_EC41_F09 - EC 41 UCLA Sample Problems#6A Sections 6.3...

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