You are interested in the prob
You are interested in the probability of the outcome whenrolling a six-sided die. Answer the following questions using p todenote the probability of this outcome.
(a) You suspect that for this die the outcome does not occurwith the same probability as with a fair die. Formulate the nulland alternative hypotheses based on which you may make astatistical inference regarding your suspicion.
(b) You suspect that for this die the outcome occurs withgreater probability than with a fair die. Formulate the null andalternative hypotheses based on which you may make a statisticalinference regarding your suspicion.
(c) You suspect that for this die the outcome occurs with lesserprobability than with a fair die. Formulate the null andalternative hypotheses based on which you may make a statisticalinference regarding your suspicion.
(d) You believe that for this die the outcome occurs with thesame 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 orto collect evidence against balancedness?
Answer:
A)
Null hypothesis, there is no significant difference in theprobability of outcome for each side of dice. Probability for eachside of dice, pi = 1/6
Alternative hypothesis, there is a significant difference in theprobability of outcome for at least one side of dice. Theprobability of at least one side of dice, pi =/= 1/6
B)
Null hypothesis, there is no significant difference in theprobability of outcome for each side of dice. probability of eachside of dice, pi = 1/6
Alternative hypothesis, for at least one side of the dice, theprobability of outcome is greater than 1/6. The probability of Atleast one side of the dice, pi > 1/6
C)
Null hypothesis, there is no significant difference in theprobability of outcome for each side of dice. probability of eachside of dice, pi = 1/6
Alternative hypothesis, for at least one side of the dice, theprobability of outcome is less than 1/6. The probability of Atleast one side of the dice, pi < 1/6
D)
The experiment can be conducted 50 times, the outcome on eachtrial should be recorded. On the basis of this outcome, theprobability 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 thishypothesis.
in hypothesis testing, it is assumed that the null hypothesis istrue. The null hypothesis is a nutrient statement about thepopulation parameter. Hence it is easier to collect evidence infavor of balancedness
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