Exercise: Testing of Hypothesis (for the students of fourth semester)

1. Suppose you are counting the number of misprints per page in a book. You want to check whether or not the average number of misprint per page is greater than 1.

(a) What will be your study variable? What will be the probability distribution of that variable?

(b) How will you collect observations? Do you examine all the pages?

(c) What will be the null and alternative hypothesis?

(d) Suppose you have decided that if you get more than 1.25 misprints per page on an average then you consider that the book has a misprint per page on an average. What is the chance of committing Type I error with your decision-making rule?

(e) Can you find the chance of committing Type II error?

2. Suppose your brother wants to play a gambling game with you. He has come up with a dice and a game plan. The game is that the dice will be rolled once if any even number appears on the top then he will pay you Rs. 100 otherwise you have to pay him Rs. 100. You suspect that your brother is using a loaded dice so that he can win. To check whether the dice is fair or not, you want to roll it 10 times before the game. If you find the dice is fair then you will play.

(a) In this context, what is your study variable? What is the probability distribution of it?

(b) What will be your null and alternative hypothesis?

(c) Suppose you have made up your mind that if you get even numbers at least 6 times then you will play. What is the chance of rejecting a fair dice with this decision rule?

(d) Suppose your brother has come up with loaded dice. The probability that the dice shows odd numbers on the top surface is 70%. With your decision rule, what is the chance that you will fall in the trap of this loaded dice?