### Hypothesis Test for the Difference Between Two Population Proportions**Overview:**A state housing department is attempting to ascertain if housing prices in County B are lower than those in County A. The department conducted a random sampling of recently sold houses in both counties, focusing on houses sold for more than $250,000. Given that County A is significantly larger than County B, a larger sample was drawn from County A. The data collected is summarized below.**Data Summary:**| | County A | County B ||----------------------|--------------------|------------------|| **Successes** | 366 | 192 || **Observations** | 700 | 400 || **p-hat** | 0.523 | 0.48 |**Statistical Analysis:**- **Confidence Level:** 90%- **z-score:** -1.372- **p-value:** 0.085**Graphical Representation:**- A normal distribution curve is displayed with a shaded region corresponding to the z-score of -1.372. This shaded area indicates the region of rejection for the hypothesis test at a 90% confidence level.### Detailed Explanation:The hypothesis test aims to determine if the proportion of houses sold for more than $250,000 in County B is significantly lower than in County A. The sample data provides the following:1. **Sample Sizes and Proportions:** - County A: - Sample Size ($ n_1 $) = 700 - Sample Proportion ($ \hat{p}_1 $) = 0.523 - County B: - Sample Size ($ n_2 $) = 400 - Sample Proportion ($ \hat{p}_2 $) = 0.482. **Hypothesis Testing:** - Null Hypothesis ($ H_0 $): No difference in the proportions ($ p_1 = p_2 $) - Alternative Hypothesis ($ H_a $): Proportion is greater in County A than in County B ($ p_1 > p_2 $)3. **Analysis and Interpretation:** - Given the z-score of -1.372 and the p-value of 0.085 at a 90% confidence level, the p-value exceeds the common significance level

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A state housing department is trying to determine if housing prices in county B are lower than in county A. The department decides to randomly sample recently sold houses in both counties and determine what proportion sold for more than $250,000. Since county A is considerably larger than county B, the housing department chose a larger sample from county A. The results of the data collected are shown below. County A County B Successes 366 Successes 192 Observations 700 Observations 400 p-hat_1 0.523 p-hat_2 0.48 p= Ex: 1.234 Confidence level 90% z-score -1.372 p-value 0.085 1 2 3 County A samples: n₁ = Ex: 9 County B samples: n₂ = Sample proportion for county A samples: p₁ = Ex: 1.234 Sample proportion for county B samples: p2 = -3 -2 z = Ex: 1.234 -1