Conduct the hypothesis test and provide the test statistic, critical value and P
ID: 3152518 • Letter: C
Question
Conduct the hypothesis test and provide the test statistic, critical value and P-value, and state the conclusion. A person drilled a hole in a die and filled it with a lead weight, then proceeded to roll it 200 times. Here are the observed frequencies for the outcomes of 1, 2, 3, 4, 5, and 6, respectively: 27, 32, 41, 41, 26, 33. Use a 0.01 significance level to test the claim that the outcomes are not equally likely. Does it appear that the loaded die behaves differently than a fair die? The test statistic is.The critical value is.The P-value is.state the conclusion. H-0.There sufficient evidence to support the claim that the outcomes are not equally likely. The outcomes to be equally likely, to behave differently from a fair die.Explanation / Answer
Here we have to test the hypothesis that,
H0 : Outcomes are equally likely.
H1 : Outcomes are not equally likely.
Assume alpha = level of significance = 0.01
We are given that outcomes and their observed frequencies.
We know that distribution of tossing a single die is Uniform.
So probability of each putcome is same.
P(1) = P(1) = P(3) = P(4) = P(5) = P(6) = 1/6 = 0.1667
These are the probabilities of each outcome.
So the complete table of x and p is,
And the test statistic is,
X2 = (O - E)2 / E
where O is observed frequency and
E is expected frequency.
These probabilities we apply for calculating expected frequency.
The formula of expected frequency is,
E = N*p
where N = number of times die roll.
The table of x, observed frequency and expected frequency is,
The test statistic is,
X2 = 6.4
P-value we can find by using EXCEL.
syntax is,
=CHIDIST(x, deg_freedom)
where x is test statistic value.
deg_freedom = n-1 = 6 - 1 = 5
P-value = 0.2692
Critical value also we can find by using EXCEL.
syntax is,
=CHIINV(probability, deg_freedom)
where probability = alpha/2
deg_freedom = n-1
critical value = 16.7496
X2 < critical value or P-value > alpha
Accept H0 at 1% level of significance.
Conclusion : : There is sufficient evidence to say that outcomes are equally likely.
x p 1 0.166667 2 0.166667 3 0.166667 4 0.166667 5 0.166667 6 0.166667 total 1