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 p>1/2. We perform a test with significance level 5%. Let n=10. For which values of Xobs 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?) Mark all appropriate values.

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 two digits after the decimal point.

What is the probability to not reject null hypothesis in this case? Enter numeric value with 2 digits after the decimal point.

What is the power of our test under these conditions? Enter numeric value with 2 digits after the decimal point.

What is the power of our test if p equals to 3/4? Enter numeric value with 2 digits after the decimal point.