SOLUTION: The policy of Banko Metro is that its ATM’s must be stocked with enough cash to satisfy customers making withdrawals over an entire weekend. An analysis of all withdrawals from

Question 1177144: The policy of Banko Metro is that its ATM’s must be stocked with enough cash to satisfy customers
making withdrawals over an entire weekend. An analysis of all withdrawals from two branches is shown in
the table below. Test at α = 0. 01 significance
Branch Mean μ Standard Deviation θ N
A Php6,800.00 Php1,200.00 2500
B Php6,790.00 Php1,400.00 2000

Answer by CPhill(1959) (Show Source): You can put this solution on YOUR website!
It appears you're asking to compare the average withdrawals at two bank branches to determine if there's a significant difference in the amount of cash needed in their ATMs. Here's how we can approach this hypothesis test:
**1. Define Hypotheses:**
* **Null Hypothesis (H0):** The mean withdrawal amounts at Branch A and Branch B are equal. (μA = μB)
* **Alternative Hypothesis (H1):** The mean withdrawal amounts at Branch A and Branch B are not equal. (μA ≠ μB)
**2. Significance Level:**
* α = 0.01
**3. Test Statistic:**
Since we have large sample sizes (nA = 2500, nB = 2000) and we know the sample standard deviations, we can use a two-sample z-test for comparing means. The test statistic is calculated as:
```
z = (x̄A - x̄B) / √((σA²/nA) + (σB²/nB))
```
where:
* x̄A and x̄B are the sample means for Branch A and Branch B, respectively.
* σA and σB are the sample standard deviations for Branch A and Branch B, respectively.
* nA and nB are the sample sizes for Branch A and Branch B, respectively.
**4. Calculate the Test Statistic:**
Plugging in the given values:
```
z = (6800 - 6790) / √((1200²/2500) + (1400²/2000))
z ≈ 0.88
```
**5. Determine the Critical Value:**
For a two-tailed test with α = 0.01, the critical z-value is approximately ±2.576 (you can find this using a z-table or calculator).
**6. Decision:**
Since the calculated z-value (0.88) falls within the critical region (-2.576 to 2.576), we fail to reject the null hypothesis.
**7. Conclusion:**
At the 1% significance level, there is not enough evidence to conclude that there is a significant difference in the mean withdrawal amounts between Branch A and Branch B. This suggests that Banko Metro can likely stock the ATMs at both branches with a similar amount of cash to satisfy customers over the weekend.
**Additional Considerations:**
* **Assumptions:** This test assumes that the withdrawal amounts at each branch are normally distributed or that the sample sizes are large enough for the Central Limit Theorem to apply.
* **Practical Significance:** Even though the statistical test did not show a significant difference, it's always a good idea to consider the practical significance of the difference in means (10 pesos) in the context of the business decision.
Let me know if you have any other questions or would like to explore this further!
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