Consider binomial test (like we discussed on the previous week). Let X be binomially distributed random variable with n trials and probability of succcess p. Null hypothesis is p=1/2, alternative is p1/2. We perform a test with significance level 5%. Let =10. For which values of sampled from X would you reject null hypothesis? (In other words: how many times a magician have to guess the result of coin tossing correctly if we toss a coin 10 times?)

Assume that correct value of p equals to 2/3 (but you don't know it). What is the probability to reject null hypothesis using the criteria you stated in the previous question? Enter numeric value with 8 digits after the decimal point.

What is the power of our test under these conditions? Enter numeric value with 8 digits after the decimal point.

What is the power of our test if p equals to 3/4? Enter numeric value with 6 digits after the decimal point.