Question

You are interested in the probability of the outcome when rolling a six-sided die. Answer the following questions using p to denote the probability of this outcome.

(a) You suspect that for this die the outcome does not occur with the same probability as with a fair die. Formulate the null and alternative hypotheses based on which you may make a statistical inference regarding your suspicion.

(b) You suspect that for this die the outcome occurs with greater probability than with a fair die. Formulate the null and alternative hypotheses based on which you may make a statistical inference regarding your suspicion.

(c) You suspect that for this die the outcome occurs with lesser probability than with a fair die. Formulate the null and alternative hypotheses based on which you may make a statistical inference regarding your suspicion.

(d) You believe that for this die the outcome occurs with the same probability as with a fair die.

How might you collect evidence in support of your belief?

Which is easier: to collect evidence in favor of balancedness or to collect evidence against balancedness?

Answer 1

A)

Null hypothesis, there is no significant difference in the probability of outcome for each side of dice. Probability for each side of dice, pi = 1/6

Alternative hypothesis, there is a significant difference in the probability of outcome for at least one side of dice. The probability of at least one side of dice, pi =/= 1/6

B)

Null hypothesis, there is no significant difference in the probability of outcome for each side of dice. probability of each side of dice, pi = 1/6

Alternative hypothesis, for at least one side of the dice, the probability of outcome is greater than 1/6. The probability of At least one side of the dice, pi > 1/6

C)

Null hypothesis, there is no significant difference in the probability of outcome for each side of dice. probability of each side of dice, pi = 1/6

Alternative hypothesis, for at least one side of the dice, the probability of outcome is less than 1/6. The probability of At least one side of the dice, pi < 1/6

D)

The experiment can be conducted 50 times, the outcome on each trial should be recorded. On the basis of this outcome, the probability of occurrence of each side of dice can be calculated. These results will correspond to my sample results.

One sample Z test for proportions can be used to test this hypothesis.

in hypothesis testing, it is assumed that the null hypothesis is true. The null hypothesis is a nutrient statement about the population parameter. Hence it is easier to collect evidence in favor of balancedness