To test the hypothesis, we will use a t-test for the sample mean. Here are the steps:

1. **State the hypotheses:**
- Null hypothesis (H0): µ = 300 hours
- Alternative hypothesis (H1): µ ≠ 300 hours

2. **Determine the significance level (α):**
- α = 0.05

3. **Calculate the test statistic:**
- The formula for the t-test statistic is:
$$
t = \frac{\bar{x} - \mu}{s / \sqrt{n}}
$$
where:
- $\bar{x}$ is the sample mean (280 hours)
- $\mu$ is the population mean under the null hypothesis (300 hours)
- $s$ is the sample standard deviation (24 hours)
- $n$ is the sample size (15)

Plugging in the values:
$$
t = \frac{280 - 300}{24 / \sqrt{15}} = \frac{-20}{24 / 3.872} = \frac{-20}{6.196} \approx -3.23
$$

4. **Determine the degrees of freedom:**
- Degrees of freedom (df) = n - 1 = 15 - 1 = 14

5. **Find the critical t-value:**
- For a two-tailed test with α = 0.05 and df = 14, the critical t-values are approximately ±2.145.

6. **Compare the test statistic to the critical t-values:**
- The calculated t-value is -3.23, which is less than -2.145.

7. **Make a decision:**
- Since the calculated t-value (-3.23) is outside the range of the critical t-values (±2.145), we reject the null hypothesis.

Therefore, the correct conclusion is:

a. reject H0.

Question

To test the hypothesis, we will use a t-test for the sample mean. Here are the steps:

1. **State the hypotheses:**
   - Null hypothesis (H0): µ = 300 hours
   - Alternative hypothesis (H1): µ ≠ 300 hours

2. **Determine the significance level (α):**
   - α = 0.05

3. **Calculate the test statistic:**
   - The formula for the t-test statistic is:
     $$
     t = \frac{\bar{x} - \mu}{s / \sqrt{n}}
     $$
     where:
     - $\bar{x}$ is the sample mean (280 hours)
     - $\mu$ is the population mean under the null hypothesis (300 hours)
     - $s$ is the sample standard deviation (24 hours)
     - $n$ is the sample size (15)

Plugging in the values:
   $$
   t = \frac{280 - 300}{24 / \sqrt{15}} = \frac{-20}{24 / 3.872} = \frac{-20}{6.196} \approx -3.23
   $$

4. **Determine the degrees of freedom:**
   - Degrees of freedom (df) = n - 1 = 15 - 1 = 14

5. **Find the critical t-value:**
   - For a two-tailed test with α = 0.05 and df = 14, the critical t-values are approximately ±2.145.

6. **Compare the test statistic to the critical t-values:**
   - The calculated t-value is -3.23, which is less than -2.145.

7. **Make a decision:**
   - Since the calculated t-value (-3.23) is outside the range of the critical t-values (±2.145), we reject the null hypothesis.

Therefore, the correct conclusion is:

a. reject H0.

Knowee AI · Accepted Answer