Answer:
p < α
0.01297 < 0.05
Since the p value is less than the α value therefore, we reject the null hypothesis so we have evidence to conclude that the die is biased.
Explanation:
H₀: The die is not biased
Ha: The die is biased
We can apply binomial distribution and determine whether the die is biased or not. (we can also perform z-test, it will provide similar results)
We know that a binomial distribution is given by
P(x; n, p) = nCx pˣ (1 - p)ⁿ⁻ˣ
Where p is the probability of success and 1 - p is the probability of failure, n is number of trials and x is the variable of interest.
For the given problem,
Total trials are n = 30
When you roll a die, there are total 6 possible outcomes,
The probability of getting the face containing two pips on each trial is
p = 1/6
p = 0.1667
The variable of interest is x = 10
P(10; 30, 0.1667) = ³⁰C₁₀*0.1667¹⁰*(1 - 0.1667)³⁰⁻¹⁰
P(10; 30, 0.1667) = (30045015)*(0.1667)¹⁰*(0.8333)²⁰
P(10; 30, 0.1667) = 0.01297
Assuming that the level of significance is α = 0.05 then
p < α
0.01297 < 0.05
Since the p value is less than the α value therefore, we reject the null hypothesis so we have evidence to conclude that the die is biased.
