Lu tells you he ipped a coin n times and recorded the number of heads he observed. He then repeated this experiment 1000 times and gives you the...

We wish to test if Lu is telling the truth about how this data was collected (did the data really come from flipping a coin?).

(a) Find the MLEs of n and p under H0. Be sure to write out the hypotheses that you are testing. Using R to get numerical approximations is okay.

(b) Calculate the expected counts.

(c) Calculate the appropriate test statistic and state its distribution under H0.

(d) Calculate the p−value of this test and make you conclusions.