Question 1174678
Here's how to solve this hypothesis test problem:

**1. Set up Hypotheses**

* **Null Hypothesis (H0):** μ ≤ 3000 (The average monthly balance is less than or equal to P3,000)
* **Alternative Hypothesis (HA):** μ > 3000 (The average monthly balance is higher than P3,000)

**2. Determine the Test Statistic**

* Since the sample size (n = 150) is large, we can use the t-test.
* The formula for the t-statistic is:
    * t = (x̄ - μ) / (s / √n)
    * Where:
        * x̄ = sample mean (4170)
        * μ = population mean (3000)
        * s = sample standard deviation (1182.50)
        * n = sample size (150)

**3. Calculate the Test Statistic**

* t = (4170 - 3000) / (1182.50 / √150)
* t = 1170 / (1182.50 / 12.247)
* t = 1170 / 96.55
* t = 12.12

**4. Determine the Critical Value**

* Significance level (α) = 0.05
* Degrees of freedom (df) = n - 1 = 150 - 1 = 149
* Because this is a right-tailed test, we need to find the critical t-value that corresponds to an area of 0.05 in the right tail of the t-distribution with 149 degrees of freedom.
* Using a t-table or calculator, the critical t-value is approximately 1.656.

**5. Make a Decision**

* Compare the calculated t-statistic (12.12) with the critical t-value (1.656).
* Since 12.12 > 1.656, we reject the null hypothesis.

**6. State the Conclusion**

* There is sufficient evidence at the 0.05 level of significance to conclude that the average monthly balance of credit card holders is higher than P3,000.