Hypothesis Testing: Sig. Level & Power of Test

[cse63146]

Homework Statement

Let X have a binomial distribution with the number of trails n = 10 and with p either 0.25 or 0.5. The simple null hypothesis p = 0.5 is rejected and the alternate hypothesis p = 0.25 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.

Homework Equations

The Attempt at a Solution

I believe that the power function is P(X<3) = P(Bin(10,0.25) < 3) and the significane leve would be $$= \alpha = P_{H_0}(_{10}C_i 0.5^{10}0.5^{10-i}<3) = 0.171875$$

Is this correct?

 

[mighty2000]

Thank you for your post. Your understanding of the power function and significance level is correct. The power function is the probability of rejecting the null hypothesis when the alternative hypothesis is true, and in this case it is the probability of observing a value less than or equal to 3 when the true probability is 0.25. The significance level is the probability of rejecting the null hypothesis when it is actually true, and in this case it is the probability of observing a value less than or equal to 3 when the true probability is 0.5.

Your calculation for the significance level is also correct. To find the significance level, we need to calculate the probability of observing a value less than or equal to 3 when the null hypothesis is true. This can be done by using the binomial distribution formula and summing the probabilities of all possible outcomes less than or equal to 3.

I hope this helps clarify your understanding of the concepts. Let me know if you have any further questions.