A die that is fair will have each face of the die come up one-sixth of the time in the long run. The population for die throwing contains the results of throwing the die an infinite number of times. For this problem, the parameter of interest is p is the probability of rolling a 4, which is the proportion of all tosses in the population that have a 4 showing on the upturned face of the die.

Question

Suppose that you have a die that may or may not be fair. On a rainy day, you toss the die 1500 times and record the outcome of each toss. After many hours and a tired arm, you found that you had rolled 282 fours. Using the following steps, conduct a hypothesis test to determine the strength of the evidence that the die is not fair.

Ho: p=1/6
Ha: p not equal to 1/6

What is the z-statistic for this test?

Answer 1

SE of proportion = sq rt of (pq/n)

when p = proprotion of 6s
and q = proportion of other values

I hope this helps.

Answer 2

A card is picked at random from a pack of 20 cards numbered 1-20. given that the cards shows an even number, find the probability that it is a multiple of 4