hypothesis testing

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#1
Jessica is trying to find out whether a particular coin is biased,so she performs a significance test. She decides that she will say that the coin is biased in favor of heads if ,when she tosses it 15 times , at least 2/3 of the tosses result in head.

a) what significance level did she use for her test?
b) what is the probability that she makes a type 1 error
c) if , in fact the coin is biased , with probability of 0.7 of obtaining a head, what is the probability that she makes a type 2 error?

let X be the result 'head' when a coin is tossed
null hypothesis : p = 0.5
alternative hypothesis : p = ?? i don't know what to write for the alternative hypothesis, is it p > 0.5?)

if the null hypothesis is true , X ~ Bin ( 15 , 0.5)

it says 2/3 of the tosses , so P (X ≥ 10) < ?? what is the significance level? should i use 0.05?

Cant do part b) and c) since i don't know how to complete par a)
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2 years ago
#2
(Original post by Carlos Nim)
Jessica is trying to find out whether a particular coin is biased,so she performs a significance test. She decides that she will say that the coin is biased in favor of heads if ,when she tosses it 15 times , at least 2/3 of the tosses result in head.

a) what significance level did she use for her test?
b) what is the probability that she makes a type 1 error
c) if , in fact the coin is biased , with probability of 0.7 of obtaining a head, what is the probability that she makes a type 2 error?

let X be the result 'head' when a coin is tossed
null hypothesis : p = 0.5
alternative hypothesis : p = ?? i don't know what to write for the alternative hypothesis, is it p > 0.5?)

if the null hypothesis is true , X ~ Bin ( 15 , 0.5)

it says 2/3 of the tosses , so P (X ≥ 10) < ?? what is the significance level? should i use 0.05?

Cant do part b) and c) since i don't know how to complete par a)
The significance level is equivalent to the probability of a trial with an unbiased coin yielding a result in the critical region. In this case, it is P(>=10 heads out of 15 tosses).
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#3
(Original post by old_engineer)
The significance level is equivalent to the probability of a trial with an unbiased coin yielding a result in the critical region. In this case, it is P(>=10 heads out of 15 tosses).
ok ok now i understand it
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