Part 2 and 3 Andre recenty found a die (the traditional, six-sided variety) at thepark. He took it home and rolled it 100 times and recorded theresults (found in the table below). Is this a 'fair die' or has it beentampered with? Test at the a = 0.05 level of significance.Which would be correct hypotheses for this test?O Ho: The die is a fair die; H,: The die has been tampered withHo: P1 = P2; H1:P1 + P2Ho: 41 = H2; H1 : µ1 # µ2| Ho: The die has been tampered with; H:The die is a fair dieRoll count:RolledCount13.35686Test Statistic (2 decimals):Give the P-value (4 decimals):Which is the correct result:Do not Reject the Null HypothesisO Reject the Null HypothesisWhich would be the appropriate conclusion?There is not enough evidence to suggest that the die has beentampered with.O There is enough evidence to suggest that the die has beentampered with.

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Description: Part 2 and 3 Andre recenty found a die (the traditional, six-sided variety) at thepark. He took it home and rolled it 100 times and recorded theresults (found in the table below). Is this a 'fair die' or has it beentampered with? Test at the a = 0.05

Answered: Test Statistic (2 decimals): Give the…

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Part 2 and 3

Andre recenty found a die (the traditional, six-sided variety) at the
park. He took it home and rolled it 100 times and recorded the
results (found in the table below). Is this a 'fair die' or has it been
tampered with? Test at the a = 0.05 level of significance.
Which would be correct hypotheses for this test?
O Ho: The die is a fair die; H,: The die has been tampered with
Ho: P1 = P2; H1:P1 + P2
Ho: 41 = H2; H1 : µ1 # µ2
| Ho: The die has been tampered with; H:The die is a fair die
Roll count:
Rolled
Count
1
3.
3
5
6
86
Test Statistic (2 decimals):
Give the P-value (4 decimals):
Which is the correct result:
Do not Reject the Null Hypothesis
O Reject the Null Hypothesis
Which would be the appropriate conclusion?
There is not enough evidence to suggest that the die has been
tampered with.
O There is enough evidence to suggest that the die has been
tampered with.

Expert Solution

Step 1

Part 2.

Assume the equal proportion. The die is rolled 100 time. The proportion rolling 1 is 16.6667 $(= \frac{1}{6} \times 100)$ . For other values also having the sample expected value.

The expected value is,

Rolled	Count	Expected
1	0	16.6667
2	5	16.6667
3	3	16.6667
4	5	16.6667
5	1	16.6667
6	86	16.6667

The test statistic is,

$\begin{array}{rcl} χ^{2} & = & S u m o f [\frac{{(O b s e r v e d c o u n t - E x p e c t e d c o u n t)}^{2}}{E x p e c t e d c o u n t}] \\ = & \frac{{(0 - 16.6667)}^{2}}{16.6667} + \frac{{(5 - 16.6667)}^{2}}{16.6667} + \frac{{(3 - 16.6667)}^{2}}{16.6667} + \frac{{(5 - 16.6667)}^{2}}{16.6667} + \frac{{(1 - 16.6667)}^{2}}{16.6667} + \frac{{(0 - 16.6667)}^{2}}{16.6667} \\ = & 16.667 + 8.167 + 11.207 + 8.167 + 14.727 + 288.427 \\ = & 347.362 \\ \approx & 347.36 \end{array}$

Thus, the test statistic is 347.36.

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