type 2 error

[crude mantle]

how to do part B

[forest knoll]

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[tribal imp]

Well, this is just a guess, but I suspect you do it by finding the probability of a Type II error.

[crude mantle]

how do we do that?

😅

it says its accepted if there is at least one tail

so do we find 1-(probability of getting no tails)

using the correct distribution

[tribal imp]

Well, first we recall the definition of a Type II error, then we calculate the probability of one occurring.

[crude mantle]

yeah I am familiar

with the definition

so do we find 1-(probability of getting no tails)
using the correct distribution

all we know about the correct distribution is that p>0.5

so how do we then find the probability/

[tribal imp]

Can you explain the definition?

[crude mantle]

when we dont reject the null hypothesis

even though we were supposed to

[tribal imp]

The null hypothesis in this case being that the coin is fair?

[crude mantle]

in this case we didn't reject it is a fair coin when we were supposed to

yep

[tribal imp]

So then we're looking for the probability that the coin is unfair and our test tells us that the coin is fair.

Under what conditions does the test tell us the coin is fair?

[crude mantle]

getting one tail

at least

[tribal imp]

And what's the probability of that occurring if the coin is not fair?

[crude mantle]

0

oh

ty!

[tribal imp]

Right, this is either a joint or a conditional probability, depending on how precisely we're talking about it.

It's either P(double headed & tails) or P(tails | double headed).

Which one is irrelevant in this specific context, since P(tails | double headed) = 0 and P(double headed & tails) = P(tails | double headed) * P(double headed).

Given that we aren't given probabilities for our hypotheses, I would suspect that we're specifically looking for the conditional probability.