se a 0.05 level of significance and te: tate the null and alternative hypothe : The two populations of sala O Ho H : The two populations of sala Median salary for public ac Ho H Median salary for public ac O H: The two populations of sa The two populations of sa O H: Median salary for public : Median salary for public a H O Hn: Median salary for public H Median salary for public Find the value of the test statistic. = M Find the p-value. (Round your ans p-value = What is your conclusion? O Reject Hn: There is not suf O Do not reject H There is O Do not reject H There is
Permutations and Combinations
If there are 5 dishes, they can be relished in any order at a time. In permutation, it should be in a particular order. In combination, the order does not matter. Take 3 letters a, b, and c. The possible ways of pairing any two letters are ab, bc, ac, ba, cb and ca. It is in a particular order. So, this can be called the permutation of a, b, and c. But if the order does not matter then ab is the same as ba. Similarly, bc is the same as cb and ac is the same as ca. Here the list has ab, bc, and ac alone. This can be called the combination of a, b, and c.
Counting Theory
The fundamental counting principle is a rule that is used to count the total number of possible outcomes in a given situation.
The second slide is the first part of the question and the first slide is the second part of the question.
![**Use a 0.05 level of significance and test the hypothesis that there is no difference between the starting annual salaries.**
**State the null and alternative hypotheses:**
- \( H_0 \): The two populations of salaries are identical.
- \( H_1 \): The two populations of salaries are not identical.
1) \( H_0 \): Median salary for public accountants = median salary for financial planners.
\( H_1 \): Median salary for public accountants \(\neq\) median salary for financial planners.
2) \( H_0 \): Median salary for public accountants - median salary for financial planners = 0.
\( H_1 \): Median salary for public accountants - median salary for financial planners \(\neq\) 0.
3) \( H_0 \): Median salary for public accountants - median salary for financial planners \(\leq\) 0.
\( H_1 \): Median salary for public accountants - median salary for financial planners > 0.
4) \( H_0 \): Median salary for public accountants - median salary for financial planners \(\geq\) 0.
\( H_1 \): Median salary for public accountants - median salary for financial planners < 0.
**Find the value of the test statistic:**
---
**Table: Starting Annual Salaries**
| **Public Accountant** | **Financial Planner** |
|-----------------------|-----------------------|
| 50.9 | 48.9 |
| 56.0 | 51.8 |
| 60.5 | 51.9 |
| 55.0 | 48.7 |
| 57.2 | 52.6 |
| 55.2 | 50.9 |
| 58.2 | 49.2 |
| | 52.1 |
| | 48.0 |
The table displays the starting annual salaries of public accountants and financial planners. Each column represents the salaries for one group, indicating a comparison of salary distributions for hypothesis testing.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F70237df8-dfb4-41d0-af11-e6f29414ce12%2F245296de-45da-404e-907a-4a90bc86257a%2Fmvfl2i_processed.jpeg&w=3840&q=75)
![### Hypothesis Testing for Salary Differences
**Objective:**
Use a 0.05 level of significance to test the hypothesis that there is no difference between the starting annual salaries of public accountants and financial planners.
#### Step 1: State the Null and Alternative Hypotheses
- **Option 1:**
- \( H_0 \): The two populations of salaries are identical.
- \( H_a \): The two populations of salaries are not identical.
- **Option 2:**
- \( H_0 \): Median salary for public accountants = Median salary for financial planners.
- \( H_a \): Median salary for public accountants ≠ Median salary for financial planners.
- **Option 3:**
- \( H_0 \): Median salary for public accountants ≤ Median salary for financial planners.
- \( H_a \): Median salary for public accountants > Median salary for financial planners.
- **Option 4:**
- \( H_0 \): Median salary for public accountants ≥ Median salary for financial planners.
- \( H_a \): Median salary for public accountants < Median salary for financial planners.
#### Step 2: Conduct the Test
**Find the value of the test statistic:**
- \( W = \) [Enter value]
**Find the p-value (Round your answer to four decimal places):**
- p-value = [Enter value]
#### Step 3: Make a Conclusion
**What is your conclusion?**
- Reject \( H_0 \): There is sufficient evidence to conclude that there is a significant difference between the starting annual salaries of public accountants and financial planners.
- Do not reject \( H_0 \): There is not sufficient evidence to conclude that there is a significant difference between the starting annual salaries of public accountants and financial planners.
Use this guide to complete your hypothesis test for comparing salaries. Ensure you enter the values for the test statistic and p-value to proceed with the analytical decision.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F70237df8-dfb4-41d0-af11-e6f29414ce12%2F245296de-45da-404e-907a-4a90bc86257a%2Ftfk21s_processed.jpeg&w=3840&q=75)
![](/static/compass_v2/shared-icons/check-mark.png)
Given starting salaries of Public Accountant and Financial Advisor are:
Public Accountant(P) | Financial Advisor(F) |
50.2 | 48 |
58.8 | 50.2 |
56.3 | 52.1 |
57.2 | 56.9 |
54.2 | 52.9 |
55 | 52.6 |
51.9 | 48.7 |
60.5 | 54.9 |
56 | 51.8 |
50.9 | 48.9 |
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