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To solve this hypothesis testing problem, let’s go through the required steps. The question requires us to determine whether there is evidence that statistics students study less than the recommended 2 hours per unit.

### Given Information
1. **Population mean** \( \mu_0 = 2 \) (recommended hours).
2. **Sample data**: \( 1.2, 2, 1.1, 1, 1.8, 2.3, 0.2, 1.4, 2, 2.1, 1.2, 1.9 \).
3. **Population standard deviation** \( \sigma = 0.9 \) hours.
4. **Sample size** \( n = 12 \).
5. **Significance level** \( \alpha = 0.05 \).
6. We are conducting a **one-tailed test** since we are testing if the mean study time is *less than* 2 hours.

### Steps for Hypothesis Testing

#### Step 1: State the Hypotheses
- **Null Hypothesis \( H_0 \)**: \( \mu = 2 \)
- **Alternative Hypothesis \( H_1 \)**: \( \mu < 2 \)

#### Step 2: Calculate the Sample Mean
The sample mean \( \bar{x} \) is calculated as follows:
\[
\bar{x} = \frac{1.2 + 2 + 1.1 + 1 + 1.8 + 2.3 + 0.2 + 1.4 + 2 + 2.1 + 1.2 + 1.9}{12} = 1.5
\]

#### Step 3: Compute the Test Statistic
Since we know the population standard deviation \( \sigma \), we use the z-test statistic formula:
\[
z = \frac{\bar{x} - \mu_0}{\sigma / \sqrt{n}}
\]
Substitute the values:
\[
z = \frac{1.5 - 2}{0.9 / \sqrt{12}} = \frac{-0.5}{0.2598} \approx -1.92
\]

#### Step 4: Determine the Critical Value and p-Value
For a one-tailed test at a \( \alpha = 0.05 \) significance level:
- The critical z-value for \( \alpha = 0.05 \) is approximately \( -1.645 \).
- Since \( -1.92 < -1.645 \), we reject the null hypothesis.

The p-value for \( z = -1.92 \) is approximately 0.0274.

#### Step 5: Conclusion
Since the p-value (0.0274) is less than the significance level (0.05), we have sufficient evidence to conclude that the mean study time per unit for statistics students is less than 2 hours.

### Filling in the Answers
Based on the above calculations:
1. **H0**: \( \mu = 2 \)
2. **H1**: \( \mu < 2 \)
3. **Test Statistic**: \( z = -1.92 \)
4. **p-Value**: Approximately 0.0274
5. **Conclusion**: There is **sufficient** evidence to conclude that the population mean study time per unit for statistics students is less than 2 hours.

### Additional Fields
- **p-Value Interpretation**: If the mean study time per unit is equal to 2 hours, there is approximately a **2.74%** chance of observing a sample mean this low or lower purely by random chance.
- **Level of significance interpretation**: There’s a 5% chance of incorrectly rejecting the null hypothesis if the true mean is actually 2 hours.

Would you like any further clarification on this solution, or help with another question? 

### Relative Questions
1. How do you calculate the test statistic if the population standard deviation is unknown?
2. What is the importance of setting a significance level before conducting the test?
3. How does a one-tailed test differ from a two-tailed test in hypothesis testing?
4. Why is the p-value interpretation critical in understanding hypothesis test results?
5. What steps should be taken if the sample size is very small and the population standard deviation is unknown?

### Tip
Always verify if the problem requires a one-tailed or two-tailed test before calculating the critical values and making conclusions.

According to the Carnegie unit system, the recommended number of hours students should study per unit is 2. Nationally, the standard deviation for study hours per unit is 0.9 hours. Do statistics students study less than the recommended number of hours per unit? The data show the results of a survey of 12 statistics students who were asked how many hours per unit they studied. Assume that the distribution of the population is normal. Data: 1.2, 2, 1.1, 1, 1.8, 2.3, 0.2, 1.4, 2, 2.1, 1.2, 1.9. What can be concluded at the 0.05 level of significance?

This solution conducts a hypothesis test to determine if statistics students study less than the recommended 2 hours per unit. The data includes a sample mean calculation, test statistic, and interpretation at a 0.05 significance level. Suitable for college students learning about hypothesis testing.

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