Question: Let X have a binomial distribution with the number of trials n = 10 an

Question

Question:

Let X have a binomial distribution with the number of trials n = 10 and

with p either 1/4 or 1/2. The simple hypothesis H0 : p = 1 is rejected, and the 12

alternative simple hypothesis H1 : p = 4 is accepted, if the observed value of X1, a random sample of size 1, is less than or equal to 3. Find the significance level and the power of the test.

Answer:

So the question I have Here is about the power fuction. Just in general I dont really understand what it is, so it would be awesome if someone could explain it to me.

And also, Why are WE subtracting (1 - the Type 2 error). Could someone please explain whats going on. Thank you!

Let X have a binomial distribution with the number of trials n-10 and p =-or- It is given that, vensus H P It is given that, Ho P=-versus H1 2 4 The probability mass function of the binomial distribution is, 1n Here, n is the number of trials and P is the probability of success. Find the significance level, if probability that a random sample of size1 is less than or equal to 3 That is, find P(X, s3) P(X, s3) 55t..+ = 0.00098 + 0.00977 + + 0. 1 1 7 1 9 =0.17 Therefore, the significance level is = 0.7

Explanation / Answer

Type 2 error is the probability of accepting null hypothesis, when it is actually false. Here, we have a decision rule that states accept nll hypothesis when X > 3.

So type 2 error = P(X>3) when null is false, that is alternative hypothesis is true, that is p = 1/4

Using n=10 and p = 1/4, we find P(X>3)

And by deifinition, Power of test = 1 - Type 2 error

So power function is basically the probability of correctly reject null when it is false. So a higher value of power is desirable.

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