Could also you please show how to find Critial Values, Test Statisitc T, and the P value

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Could also you please show how to find Critial Values, Test Statisitc T, and the P value using a Calculator (TI 84) and whether it reject or fail to reject based on the evidence.

 

## Testing a University’s Class Size Claim

You receive a brochure from a large university. The brochure states that the mean class size for full-time faculty is fewer than 32 students. You wish to test this claim. To do so, you randomly select 18 classes taught by full-time faculty and determine the class size of each. The class sizes are shown in the table below. Given a significance level (α) of 0.10, can you support the university's claim? Assume the population is normally distributed.

Class sizes for randomly selected classes:
```
33, 25, 31, 30, 30, 38, 26, 25, 27, 27, 30, 36, 33, 27, 28, 31, 26, 27
```

### Steps to Test the Claim

**(a) State the Claim Mathematically and Identify \( H_0 \) and \( H_a \)**

Which of the following correctly states the null hypothesis (\( H_0 \)) and the alternative hypothesis (\( H_a \))?

- **Option A:**
  - \( H_0 \): \( \mu = 32 \)
  - \( H_a \): \( \mu < 32 \)

- **Option B:**
  - \( H_0 \): \( \mu \ge 32 \)
  - \( H_a \): \( \mu < 32 \)
  
- **Option C:**
  - \( H_0 \): \( \mu > 32 \)
  - \( H_a \): \( \mu \le 32 \)
  
- **Option D:**
  - \( H_0 \): \( \mu \le 32 \)
  - \( H_a \): \( \mu > 32 \)
  
- **Option E:**
  - \( H_0 \): \( \mu = 32 \)
  - \( H_a \): \( \mu \neq 32 \)

- **Option F:**
  - \( H_0 \): \( \mu < 32 \)
  - \( H_a \): \( \mu \ge 32 \)

**Answer:**

The correct hypotheses are represented by **Option B**:
- **Null Hypothesis (\( H_0 \))**: \( \mu \ge 32 \)
  - This means
Transcribed Image Text:## Testing a University’s Class Size Claim You receive a brochure from a large university. The brochure states that the mean class size for full-time faculty is fewer than 32 students. You wish to test this claim. To do so, you randomly select 18 classes taught by full-time faculty and determine the class size of each. The class sizes are shown in the table below. Given a significance level (α) of 0.10, can you support the university's claim? Assume the population is normally distributed. Class sizes for randomly selected classes: ``` 33, 25, 31, 30, 30, 38, 26, 25, 27, 27, 30, 36, 33, 27, 28, 31, 26, 27 ``` ### Steps to Test the Claim **(a) State the Claim Mathematically and Identify \( H_0 \) and \( H_a \)** Which of the following correctly states the null hypothesis (\( H_0 \)) and the alternative hypothesis (\( H_a \))? - **Option A:** - \( H_0 \): \( \mu = 32 \) - \( H_a \): \( \mu < 32 \) - **Option B:** - \( H_0 \): \( \mu \ge 32 \) - \( H_a \): \( \mu < 32 \) - **Option C:** - \( H_0 \): \( \mu > 32 \) - \( H_a \): \( \mu \le 32 \) - **Option D:** - \( H_0 \): \( \mu \le 32 \) - \( H_a \): \( \mu > 32 \) - **Option E:** - \( H_0 \): \( \mu = 32 \) - \( H_a \): \( \mu \neq 32 \) - **Option F:** - \( H_0 \): \( \mu < 32 \) - \( H_a \): \( \mu \ge 32 \) **Answer:** The correct hypotheses are represented by **Option B**: - **Null Hypothesis (\( H_0 \))**: \( \mu \ge 32 \) - This means
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