We reach the conclusion that an equivalent or greater proportion of Republicans support lowering the standards. Explanation: The detailed prompt reveals a national survey conducted among key Republicans and Democrats regarding their support for decreasing environmental standards to permit high-sulfur coal usage in power plants. The results indicate: a sample size of 1,000 Republicans and 800 Democrats, where 200 Republicans and 168 Democrats expressed support. The question asks if we can determine at the 0.02 significance level that there exists a larger proportion among Democrats favoring the reduction. The null hypothesis posits that an equal or larger percentage of Republicans back this change, leading to H0: p1 = p2. Conversely, the alternative hypothesis proposes that a greater fraction of Democrats endorses the lowering of standards, formulated as Ha: p2 > p1. The appropriate statistical test employed is a two-sample z-test for proportions, with the computed test statistic exhibiting a value of -0.52. This leads us to evaluate the p-value, derived from the test statistic yields, P-value = P(Z < -0.52) = 1 - P(Z > 0.52) equating to approximately 0.3015. With a significance level of 0.02, we find that the computed statistic exceeds the critical value of -2.054, which allows us insufficient evidence to reject the null hypothesis, confirming the initial conclusion that there exists an equal or larger proportion of Republicans favoring a reduction.
Answer:
Step-by-step explanation:
For resolution, the Euclidean division is necessary:
- The polynomial is expressed as 16-2x³-6x²+x+9=-2x³-6x²+x+9
- We will divide this by: 4+3x-2=3x+2 and analyze the remainder
A visual representation of the process is provided
- The remainder is 47/9, hence the value to subtract is 47/9
