Conduct a full hypothesis test and determine if the given claim is supported or not supported at the 0.05 significance level. Round all amounts and standard scores to two decimal places.
-According to a recent poll 53% of Americans would vote for the incumbent president. If a random sample of 100 people results in 25% who would vote for the incumbent, test whether the claim that the actual percentage is different from 53% is supported or not supported.
A)supported
B)not supported

Question

Quizplus · Accepted Answer

The hypothesis test involves comparing the sample proportion to the population proportion using a significance level of 0.05. The null hypothesis (H0) is that the population proportion is equal to 0.53 (p = 0.53), and the alternative hypothesis (H1) is that the population proportion is not equal to 0.53 (p ≠ 0.53), indicating a two-tailed test.To conduct the test, we calculate the z-score using the formula:$$ z = \frac{\hat{p} - p}{\sqrt{\frac{p(1-p)}{n}}} $$where:- $\hat{p}$ is the sample proportion (0.25),- $p$ is the population proportion (0.53),- $n$ is the sample size (100).Plugging in the values:$$ z = \frac{0.25 - 0.53}{\sqrt{\frac{0.53(1-0.53)}{100}}} $$$$ z = \frac{-0.28}{\sqrt{\frac{0.53(0.47)}{100}}} $$$$ z = \frac{-0.28}{\sqrt{0.2491/100}} $$$$ z = \frac{-0.28}{0.0499} $$$$ z = -5.61 $$A z-score of -5.61 is well beyond the critical values for a 0.05 significance level in a two-tailed test (approximately ±1.96), indicating that the sample proportion is significantly different from the population proportion. Therefore, the claim that the actual percentage is different from 53% is supported.

Conduct a Full Hypothesis Test and Determine If the Given