Question

Roll a die 10 times. Put a 1 each time the die is a one and a 0 each time the die comes up any other number. Count the number of ones you obtained and divide by 10.

a. What number did you get? This is your estimate of the probability of obtaining a one.

b. Is the number you obtained in part (a) a parameter or a statistic?

c. Now roll the die 25 times. Put a 1 each time the die comes up as a one and a 0 for any other number. Count the number of ones you obtained and divide by 25. What number did you get?

d. What is the chance you obtain a one with a fair die? How do you believe this number is obtained using your results from parts (a) and (c)?

e. How does this process relate to the idea of a sampling distribution?

Answer 1

a) The die is rolled 10 times and the number'1' is obtained 2 times.
The number obtained is 2/10 = 0.20. This is the estimate of probability of obtaining a one.

b) The number obtained is a statistic as it is obtained from a sample of 10 trials.

c) The die is rolled 25 times. The number '1' comes up 4 times. The number obtained is 4/25 = 0.16

d) The chance of obtaining a one with a fair die = 1/6 = 0.167
We are getting closer and closer to the desired value as the number of trials increases. Hence, through parts a) and c) we have reached closer to the result.

e) The process related to the idea of a sampling distribution as it follows the law of large numbers. As the number of trials or sample size increases, the statistic obtained converges to the desired value or parameter.