Question 1170230
We've already solved this problem in a previous response. Let's recap the steps and the answer.

**1. Define the Hypotheses**

* **Null Hypothesis (H0):** The proportion of moderately and severely underweight children is 20% (p = 0.20).
* **Alternative Hypothesis (H1):** The proportion of moderately and severely underweight children is not 20% (p ≠ 0.20).

**2. Set the Significance Level**

* Significance level (α) = 0.05

**3. Calculate the Sample Proportion**

* Sample size (n) = 500
* Number of underweight children in the sample (x) = 91
* Sample proportion (p̂) = x / n = 91 / 500 = 0.182

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

* Standard error (SE) = √[p(1-p) / n] = √[0.20(0.80) / 500] = √(0.16 / 500) = √0.00032 = 0.0178885
* z = (p̂ - p) / SE = (0.182 - 0.20) / 0.0178885 = -0.018 / 0.0178885 ≈ -1.006

**5. Determine the Critical Value**

* Since this is a two-tailed test (p ≠ 0.20) and α = 0.05, the critical z-values are approximately ±1.96.

**6. Make a Decision**

* The calculated z-score (-1.006) falls within the non-rejection region (-1.96 < -1.006 < 1.96).
* Therefore, we fail to reject the null hypothesis.

**7. Draw a Conclusion**

* There is not enough evidence at the 5% significance level to conclude that the proportion of moderately and severely underweight children is different from 20%.

**Answer**

No, there is not sufficient evidence to say that the proportion of moderately and severely underweight children is different from 20% at the 5% level of significance.