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In: Statistics and Probability
Concept Check: Test Statistics 1 point possible (graded) Setup: Recall the statistical experiment in which you...
Concept Check: Test Statistics
1 point possible (graded)
Setup:
Recall the statistical experiment in which you
flip a coin n times to decide the coin is fair.
You model the coin flips as X1,…,Xn∼iidBer(p) where p is an unknown parameter, and formulate the hypothesis:
| H0: | p=0.5 | |||
| H1: | p≠0.5, |
and design the test ψ using the statistic Tn:
| ψn | = | 1(Tn>C) | ||||
| where | Tn | = | n−−√∣∣X¯¯¯¯n−0.5∣∣0.5(1−0.5)−−−−−−−−−−√ |
where the number C is the threshold. Note the absolute value in Tn for this two sided test.
Question:
If it is true that p=1/2, which of the following are true about
Tn?
(Choose all that apply.)
Tn is a consistent estimator of the true parameter p=1/2.
limn→∞Tn−→−−n→∞(d)|Z| where Z∼N(0,1) is a standard Gaussian.
Tn involves a shift and rescaling of the sample average so that as n→∞, this random variable will converge in distribution.
The limiting distribution of Tn can be understood using computational software or tables.
unanswered
Solutions
orchestra answered 1 year agoRelated Solutions
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