Conduct the hypothesis test and provide the test statistic, critical value and P
ID: 3156728 • 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,
29,
42,
40,
29,
33.
Use a
0.025
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
nothing.
(Round to three decimal places as needed.)
Explanation / Answer
This account sfor Chi-square Goodness of Fit test.
State the hypotheses:
H0: The outcomes are equally likely.
H1: The outcomes are not equally likely.
Compute test statistic:
X^2=5.92
P value at df=(6-1)=5 is 0.314.
The p value is not less than alpha=0.025. Therefore, fail to reject null hypothesis. There is insufficient sample evidence to cocnclude that outcomes rae not equally likely.
Observed Expected (Observed-Expectde)^2/Expected 27 33.33[200*0.167] 1.2033 29 33.33 0.5633 42 33.33 2.2533 40 33.33 1.3333 29 33.33 0.5633 33 33.33 0.0033