Test Statistic (2 decimals): Give the P-value (4 decimals):
Percentage
A percentage is a number indicated as a fraction of 100. It is a dimensionless number often expressed using the symbol %.
Algebraic Expressions
In mathematics, an algebraic expression consists of constant(s), variable(s), and mathematical operators. It is made up of terms.
Numbers
Numbers are some measures used for counting. They can be compared one with another to know its position in the number line and determine which one is greater or lesser than the other.
Subtraction
Before we begin to understand the subtraction of algebraic expressions, we need to list out a few things that form the basis of algebra.
Addition
Before we begin to understand the addition of algebraic expressions, we need to list out a few things that form the basis of algebra.
Part 2 and 3
![Andre recently 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 \( \alpha = 0.05 \) level of significance.
**Which would be correct hypotheses for this test?**
- \( H_0: \) The die is a fair die; \( H_1: \) The die has been tampered with [selected]
- \( H_0: p_1 = p_2; \, H_1: p_1 \neq p_2 \)
- \( H_0: \mu_1 = \mu_2; \, H_1: \mu_1 \neq \mu_2 \)
- \( H_0: \) The die has been tampered with; \( H_1: \) The die is a fair die
**Roll count:**
\[
\begin{array}{|c|c|}
\hline
\text{Rolled} & \text{Count} \\
\hline
1 & 0 \\
2 & 5 \\
3 & 3 \\
4 & 5 \\
5 & 1 \\
6 & 86 \\
\hline
\end{array}
\]
**Test Statistic (2 decimals):**
\[ \_\_\_\_ \]
**Give the P-value (4 decimals):**
\[ \_\_\_\_ \]
**Which is the correct result:**
- Do not Reject the Null Hypothesis
- Reject the Null Hypothesis [selected]
**Which would be the appropriate conclusion?**
- There is not enough evidence to suggest that the die has been tampered with.
- There is enough evidence to suggest that the die has been tampered with. [selected]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F51b0da3b-8067-4e4b-be01-e9ec9540c1dc%2Fa3d4aa87-5014-4594-8937-15c6a349021a%2Ffdej3hp_processed.jpeg&w=3840&q=75)
Part 2.
Assume the equal proportion. The die is rolled 100 time. The proportion rolling 1 is 16.6667. 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,
Thus, the test statistic is 347.36.
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