User: It is known that if a signal of value μ is sent from location A, then the value received at location B is normally distributed with mean μ and standard deviation 3. That is, the random noise added to the signal is an N(0,9)
 random variable. There is reason for the people at location B to suspect that the signal value sent today is 
\mu=12. A hypothesis testing is conducted based on 6 independent signals received at location B at a significance level of 0.05 to determine if 
\mu=12 or 
\mu>12 . The average of the six signals is 13.1. What is the p-value (up to 2 non-zero digits)?
Group of answer choices

0.37

0.82

0.18

None of the above



It is known that if a signal of value μ is sent from location A, then the value received at location B is normally distributed with mean μ and standard deviation 3. That is, the random noise added to the signal is an N(0,9)
 random variable. There is reason for the people at location B to suspect that the signal value sent today is 
\mu=12. A hypothesis testing is conducted based on 6 independent signals received at location B at a significance level of 0.05 to determine if 
\mu=12 or 
\mu>12 . The average of the six signals is 13.1. What is the p-value (up to 2 non-zero digits)?
Group of answer choices

0.37

0.82

0.18

None of the above



It is known that if a signal of value μ is sent from location A, then the value received at location B is normally distributed with mean μ and standard deviation 3. That is, the random noise added to the signal is an N(0,9)
 random variable. There is reason for the people at location B to suspect that the signal value sent today is 
\mu=12. A hypothesis testing is conducted based on 6 independent signals received at location B at a significance level of 0.05 to determine if 
\mu=12 or 
\mu>12 . The average of the six signals is 13.1. What is the p-value (up to 2 non-zero digits)?
Group of answer choices

0.37

0.82

0.18

None of the above
Assistant:  Let'sLet's analyze the problem step by step.

### Given:
- Null hypothesis: \( H_0: \mu = 12 \)
- Alternative hypothesis: \( H_a: \mu > 12 \)
- Sample size: \( n = 6 \)
- Sample mean: \( \bar{x} = 13.1 \)
- Known standard deviation of each signal: \( \sigma = 3 \)
- Significance level: \( \alpha = 0.05 \)

---

### Step 1: Calculate the test statistic

Since \(\sigma\) is known, we can use a z-test for the mean:
\[
Z = \frac{\bar{x} - \mu_0}{\sigma / \sqrt{n}}
\]
where \(\mu_0 = 12\).

Calculate:
\[
Z = \frac{13.1 - 12}{3 / \sqrt{6}} = \frac{1.1}{3 / 2.449} = \frac{1.1}{1.2247} \approx 0.898
\]

---

### Step 2: Find the p-value

Since it is a **right-tailed test** (\( \mu > 12 \)), the p-value is:
\[
p = P(Z > 0.898)
\]

Use standard normal distribution table or calculator:

- \(P(Z < 0.898) \approx 0.8159\)
- So,
\[
p = 1 - 0.8159 = 0.1841 \approx 0.18
\]

---

### Step 3: Conclusion

- p-value \(\approx 0.18\)
- Compare p-value with \(\alpha = 0.05\).
- Since \(0.18 > 0.05\), we **fail to reject** \(H_0\).

---

### Final answer:

**The p-value is approximately 0.18.**

---

### Among options:
- 0.37
- 0.82
- 0.18
- None of the above

The correct choice is **0.18**.
User: https://www.youtube.com/watch?v=niWpfRyvs2U
Assistant:  II’m currently unable to watch or interact with YouTube videos directly. However, if you describe the content or share what you need help with from that video, I’d be happy to assist!
User: https://www.youtube.com/watch?v=niWpfRyvs2U
Assistant: