To assess anemia prevalence, a study is done to test hemoglobin levels in female residents of a rural region. The national average for all women in the country is $$ \mu=13.2 $$ grams/deciliter. The hemoglobin levels of a simple random sample of 32 female residents were collected and analyzed. Assuming the requirements are met for the hemoglobin study and $$ \alpha=0.05 $$, researchers want to test the claim that mean hemoglobin values for females in the rural region are greater than the national average. If the $$ p $$-value for the test is calculated and found to be $$ P=0.044 $$, what is the correct conclusion for this hypothesis test? Since the $$ p $$-value is less than $$ \alpha $$, we reject the null hypothesis. This means there is sufficient evidence to conclude that the mean value of women in the region have higher hemoglobin values than the national average for women. Since the $$ p $$-value is less than $$ \alpha $$, we reject the null hypothesis. This means there is insufficient evidence to conclude that the mean value of women in the region have higher hemoglobin values than the national average for women. Since the $$ p $$-value is greater than $$ \alpha $$, we fail to reject the null hypothesis. This means there is insufficient evidence to conclude that the mean value of women in the region have higher hemoglobin values than the national average for women. - Since the $$ p $$-value is greater than $$ \alpha $$, we fail to reject the null hypothesis. This means there is sufficient evidence to conclude that the mean value of womea in the region have higher hemoglobin values than the national average for women.

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The correct conclusion for the hypothesis test is: **Since the $$ p $$-value is less than $$ \alpha $$, we reject the null hypothesis. This means there is sufficient evidence to conclude that the mean value of women in the region have higher hemoglobin values than the national average for women.** **Explanation:** 1. **Hypothesis Setup:** - **Null Hypothesis ($$ H_0 $$)**: The mean hemoglobin level for women in the rural region is equal to the national average ($$ \mu = 13.2 $$ grams/deciliter). - **Alternative Hypothesis ($$ H_1 $$)**: The mean hemoglobin level for women in the rural region is greater than the national average ($$ \mu > 13.2 $$ grams/deciliter). 2. **Test Statistic and $$ p $$-value:** - A $$ p $$-value of 0.044 was calculated from the sample data. - The significance level ($$ \alpha $$) is set at 0.05. 3. **Decision Rule:** - If $$ p $$-value < $$ \alpha $$, reject $$ H_0 $$. - If $$ p $$-value ≥ $$ \alpha $$, fail to reject $$ H_0 $$. 4. **Application:** - Since 0.044 < 0.05, we **reject the null hypothesis**. 5. **Conclusion:** - Rejecting $$ H_0 $$ indicates that there is **sufficient evidence** to support the claim that the mean hemoglobin level for women in the rural region is greater than the national average. **Incorrect Options Explained:** - **Option 2:** States that rejecting $$ H_0 $$ leads to insufficient evidence, which is incorrect. - **Options 3 and 4:** Incorrectly compare the $$ p $$-value to $$ \alpha $$, suggesting $$ p $$-value > $$ \alpha $$, which is not the case here. Therefore, **Option 1** is the correct conclusion. **Correct Answer:** Since the $$ p $$-value is less than $$ \alpha $$, we reject the null hypothesis. This means there is sufficient evidence to conclude that the mean value of women in the region have higher hemoglobin values than the national average for women. Since the $$ p $$-value is less than $$ \alpha $$, we reject the null hypothesis. This means there is sufficient evidence to conclude that the mean hemoglobin levels of women in the rural region are higher than the national average.

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