Polly suspects that a die is biased. The probability of the die landing on 6 is believed to be 0.4, and Polly thinks this probability has changed. The die is to be rolled 20 times, and X X\,X is the number of sixes obtained.
Write down the hypotheses Polly should use.
Using a 10% significance level, find the critical region for a two-tailed test, with a probability of at most 0.05 in each tail.
Find the actual significance level of a test based on this critical region.
Polly rolls the die 20 times and obtains 11 sixes. Comment on Polly's suspicion.