Test the claim that a six-sided dice is fair at the 0.05 significance level. Complete the table. Round all answers to three decimal places. Number rolled on dice Observed Frequency Expected Frequency (O−E)2E(O-E)2E 1 25 2 24 3 10 4 9 5 7 6 6 H0H0: p₁ = p₂ = p₃ = p₄ = p₅ = p₆ H1H1: at least one is different Original claim = Select an answer H₀ H₁ Enter the critical value, along with the significance level and degrees of freedom χ2χ2(αα,df) below the graph. (Graph is for illustration only. No need to shade.) X2Χ2(,) = (Round to three decimal places.) Test Statistic = (Round to three decimal places.) p-value= (Round to four decimal places.) Decision: Select an answer Fail to reject the null hypothesis Reject the null hypothesis Accept the alternative hypothesis Accept the null hypothesis Conclusion: Select an answer There is not sufficient evidence to warrant rejection of There is not enough evidence to support There is sufficient evidence to warrant rejection of The sample data supports the claim that all 6 categories are equally likely to be selected.
Test the claim that a six-sided dice is fair at the 0.05 significance level. Complete the table. Round all answers to three decimal places.
| Number rolled on dice | Observed Frequency |
Expected Frequency |
(O−E)2E(O-E)2E |
|---|---|---|---|
| 1 | 25 | ||
| 2 | 24 | ||
| 3 | 10 | ||
| 4 | 9 | ||
| 5 | 7 | ||
| 6 | 6 |
H0H0: p₁ = p₂ = p₃ = p₄ = p₅ = p₆
H1H1: at least one is different
Enter the critical value, along with the significance level and degrees of freedom χ2χ2(αα,df) below the graph. (Graph is for illustration only. No need to shade.)
(Round to three decimal places.)
Test Statistic = (Round to three decimal places.)
p-value=
(Round to four decimal places.)
Decision: Select an answer Fail to reject the null hypothesis Reject the null hypothesis Accept the alternative hypothesis Accept the null hypothesis
Conclusion: Select an answer There is not sufficient evidence to warrant rejection of There is not enough evidence to support There is sufficient evidence to warrant rejection of The sample data supports the claim that all 6 categories are equally likely to be selected.
Here, the claim of the test is that six-sided dice is fair. Hence, the original claim is that six-sided dice is fair. That is, the claim is that all 6 categories are equally likely to be selected.
Here, n is 74 and p=1/6=0.167.
The table is,
|
Number rolled on dice |
Observed Frequency |
Expected frequency (E=n*p) |
(O-E)^2 |
(O-E)^2/E |
|
1 |
25 |
13.527 |
131.630 |
9.731 |
|
2 |
24 |
13.527 |
109.684 |
8.109 |
|
3 |
10 |
13.527 |
12.440 |
0.920 |
|
4 |
9 |
13.527 |
20.494 |
1.515 |
|
5 |
7 |
13.527 |
42.602 |
3.149 |
|
6 |
6 |
13.527 |
56.656 |
4.188 |
|
Total |
81 |
|
|
27.612 |
The degrees of freedom is,
Df=k-1
=6-1
=5
From the Chi square table, the critical value for the degrees of freedom is 5 with 0.05 level is 11.070.
From the table, the test statistic is 27.612.
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