Computing Type 1 Error Rate for Coin Test

[EvLer]

How would I compute the type 1 error rate of the following test:

accept that coin is fair if in 30 tosses the coin gives between 11 and 19 heads (inclusive), reject otherwise.

I guess my Ho is 11/30<p<19/30
and H1: p < 11/30 or p > 19/30

so type I prob = P(p < 11/30) + P(p > 19/30) both under Ho.
Is this correct?

thanks

 

[TripleS]

it should be right, i think

 

[tacman]

Your approach to computing the type 1 error rate is correct. Type 1 error, also known as a false positive, occurs when the null hypothesis (Ho) is rejected when it is actually true. In this case, the null hypothesis is that the coin is fair, meaning the probability of getting heads is between 11/30 and 19/30. The alternative hypothesis (H1) is that the probability of getting heads is either less than 11/30 or greater than 19/30.

To compute the type 1 error rate, you need to calculate the probability of getting a result that falls outside of the range specified by Ho. This includes both the probability of getting a result less than 11/30 and the probability of getting a result greater than 19/30. As you mentioned, this can be written as P(p < 11/30) + P(p > 19/30), both under Ho.

However, it is important to note that the actual type 1 error rate can only be determined by conducting the test and analyzing the results. The calculated probability is an estimate of the true type 1 error rate, but it may not be exact. To get a more accurate estimate, you can conduct multiple trials of this test and calculate the average type 1 error rate.

In summary, your approach to computing the type 1 error rate is correct, but keep in mind that it is an estimate and the actual rate can only be determined through experimentation.