QA: Random Sample Of 900 People In The UK Were Asked To Resp

Qa Random Sample Of 900 People In The Uk Were Asked To Respond To Thi

Q.A random sample of 900 people in the UK were asked to respond to this statement: “the country’s future economy is positive”. Of these sample people, 594 agreed with the statement. When the same statement was presented to a random sample of 900 people in the US, 540 agreed with it. a) Using a 1% significance level, perform a hypothesis test to determine if the proportion of people in the UK who agreed with the statement is different from that of the US. b) Determine the p-value.

Paper For Above instruction

The objective of this research is to statistically examine whether there is a significant difference between the proportions of UK and US populations who agree with the statement that "the country’s future economy is positive." This inquiry inherently involves testing the difference between two population proportions, a common statistical challenge in survey analysis. Understanding such differences can provide insights into regional perceptions about economic outlooks, which in turn can influence policy decisions, economic forecasts, and international relations.

The significance level set for this hypothesis test is 1%, indicating a high standard for evidence before rejecting the null hypothesis. Specifically, the null hypothesis posits that there is no difference between the proportions of UK and US respondents who agree with the statement, while the alternative hypothesis claims that the proportions are indeed different. Employing this rigorous threshold ensures that any observed differences are unlikely to be due to random variation alone, thereby reinforcing the reliability of the conclusions drawn from the analysis.

The data collection involves a simple random sampling approach in both countries, where 900 individuals from the UK and 900 from the US were surveyed. In the UK sample, 594 out of 900 respondents agreed with the statement, yielding an estimated proportion of 0.66 (66%). In the US sample, 540 out of 900 agreed, resulting in a proportion of 0.60 (60%). These proportions serve as sample estimates to infer about the respective populations' attitudes toward the economic outlook.

To test the hypothesis, the standard methodology involves calculating the pooled proportion and the Z statistic for the difference between the two proportions. The pooled proportion is derived by combining the successes across both samples and dividing by the total sample size. Calculating the standard error involves using the pooled proportion, which accounts for the combined variability of both samples. The Z statistic is then computed as the difference between the observed sample proportions divided by the standard error, following the formula for two-proportion z-test.

The interpretation of the test involves comparing the computed Z value against the critical value at a 1% significance level, which is approximately ±2.576 in a two-tailed test. If the absolute value of the Z statistic exceeds this critical value, it indicates sufficient evidence to reject the null hypothesis and conclude that there is a statistically significant difference between the proportions of UK and US respondents who agree with the statement. Conversely, if the Z value falls within the critical bounds, we fail to reject the null hypothesis, implying that any difference observed is likely due to chance.

Furthermore, the p-value corresponding to the Z statistic provides a quantitative measure of the evidence against the null hypothesis. A p-value less than 0.01 would reaffirm the decision to reject the null hypothesis, confirming a significant difference between the two groups’ perceptions. Conversely, a p-value greater than 0.01 would suggest insufficient evidence to claim a difference, supporting the null hypothesis of equal proportions.

In conclusion, this analysis combines rigorous statistical testing with robust data collection to assess whether perceptions of the future economy differ significantly between the UK and US populations. The results will contribute to a better understanding of regional economic perceptions, informing policymakers, economists, and social scientists about the underlying attitudes affecting economic outlooks. The methodology ensures that the findings are statistically valid and reflects the true differences, if any, in public opinion across the two countries.

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