Question 1184272
Here's how to perform a hypothesis test to determine if the malaria situation in 2016 was significantly different from 2015:

**1. State the Hypotheses:**

* **Null Hypothesis (H0):** There is no significant difference in the proportion of people with malaria between 2015 and 2016.  (p1 = p2)
* **Alternative Hypothesis (H1):** There is a significant difference in the proportion of people with malaria between 2015 and 2016. (p1 ≠ p2)

**2. Define the Significance Level:**

α = 0.05 (5%)

**3. Calculate the Sample Proportions:**

* **2015:**
   - p1 = 0.038 (3.8%)
   - n1 = 15,000

* **2016:**
   - Number of positive cases = 200
   - p2 = 200 / 10,000 = 0.02 (2%)
   - n2 = 10,000

**4. Calculate the Test Statistic (z-score):**

We'll use a two-proportion z-test.  The formula for the test statistic is:

z = (p1 - p2) / sqrt[ p(1-p) * (1/n1 + 1/n2) ]

Where 'p' is the pooled proportion, calculated as:

p = (x1 + x2) / (n1 + n2) = (0.038 * 15000 + 200) / (15000 + 10000) = (570 + 200) / 25000 = 770 / 25000 = 0.0308

Now, plug the values into the z-score formula:

z = (0.038 - 0.02) / sqrt[ 0.0308 * (1 - 0.0308) * (1/15000 + 1/10000) ]
z = 0.018 / sqrt[ 0.0298 * (0.0000667 + 0.0001) ]
z = 0.018 / sqrt(0.0298 * 0.0001667)
z = 0.018 / sqrt(0.000004967)
z = 0.018 / 0.002229
z ≈ 8.08

**5. Determine the Critical Value:**

Since this is a two-tailed test (H1: p1 ≠ p2) at α = 0.05, we need to find the critical z-values that correspond to the tails of the standard normal distribution.  Look up z = ±1.96.

**6. Make a Decision:**

* **Compare the test statistic to the critical values:** Our calculated z-score (8.08) is much larger than the critical value (1.96).

* **Conclusion:** Because the absolute value of the calculated z-score is greater than the critical value, we reject the null hypothesis.

**7. Interpret the Results:**

There is sufficient evidence at the 5% level of significance to conclude that there is a statistically significant difference in the proportion of people with malaria between 2015 and 2016 in Zambia.  The malaria situation in 2016 was significantly different from 2015.