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You take a random sample of size 30 and conduct a hypothesis test at the 5...

You take a random sample of size 30 and conduct a hypothesis test at the 5 % level of significance . If instead , you take a random sample of size 50 and conduct the same hypothesis test at the same 5 % level of significance , what can you say about the probability of a type I and type II error (all else being equal ) ?
A. P (Type I errror ) decreases and P (Type II error ) decreases
B. P (Type I errror ) stays the same and P(Type II error ) increases .
C. P(Type I errror ) decreases and P (Type II error ) increases
D. P(Type I errror ) stays the same and P(Type II error ) decreases

math   Statistics-And-Probability   
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Answer #1

You take a random sample of size 30 and conduct a hypothesis test at the 5 % level of significance . If instead , you take a random sample of size 50 and conduct the same hypothesis test at the same 5 % level of significance ,

P(Type I errror ) decreases and P (Type II error ) increases...hence C is the answer...

Justification--

The larger probability of rejecting the null hypothesis decreases the probability of committing a type II error while the probability of committing a type I error increases....and vice versa...

Note-if there is any understanding problem regarding this please feel free to ask via comment box ..thank you

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