Question 1171395
Let's break down this hypothesis test and determine the appropriate distribution.

**1. Define the Problem:**

* **Null Hypothesis (H0):** The new test program Y is not better than the original program X. The error rate of Y is the same as or less than 1% (0.01).
* **Alternative Hypothesis (H1):** The new test program Y is better than the original program X. The error rate of Y is greater than 1% (0.01).
* **Significance Level (α):** 5% or 0.05.

**2. Data:**

* **Original Program X:** Error rate (p0) = 0.01
* **New Program Y:**
    * Number of trials (n) = 50
    * Number of errors (x) = 2
    * Sample proportion (p̂) = x/n = 2/50 = 0.04

**3. Choose the Appropriate Distribution:**

* Since we're dealing with proportions and a relatively large sample size (n=50), we can use the **normal distribution** to approximate the binomial distribution.

**4. Calculate the Standard Error:**

* The standard error (SE) for a proportion is calculated as:
    * SE = √(p0(1 - p0) / n)
    * SE = √(0.01(1 - 0.01) / 50)
    * SE = √(0.01(0.99) / 50)
    * SE = √(0.0099 / 50)
    * SE = √0.000198
    * SE ≈ 0.01407

**5. State the Distribution:**

* P' ~ N (p0, SE^2)
* P' ~ N (0.01, 0.01407^2)
* P' ~ N (0.01, 0.000198)

Therefore, the distribution to use for the test is:

P' ~ N (0.0100, 0.000198)