Traditionally 2 Percent Of The Citizens Of The United States

Traditionally 2 Percent Of The Citizens Of The United States Live In

Traditionally, 2 percent of the citizens of the United States live in a foreign country because they are disenchanted with U.S. politics or social attitudes. In order to test if this proportion has increased since the September 11, 2001, terror attacks, U.S. consulates contacted a random sample of 400 of these expatriates. The sample yields 12 people who report they are living overseas because of political or social attitudes. Can you conclude this data shows the proportion of politically motivated expatriates has increased?

a) State the null and alternative hypothesis.

b) Calculate the test statistic. Show your calculation.

c) Determine the p-value.

d) What is your decision regarding the null statement if α = 0.05?

e) Write a conclusion statement.

Paper For Above instruction

The proportion of U.S. citizens living abroad due to discontent with domestic political or social issues is a pertinent indicator assessing the impact of national events on expatriate behavior. This study aims to determine whether the proportion of such expatriates has increased since the September 11, 2001 terrorist attacks. Using a sample of 400 expatriates, surveyed by the U.S. consulates, with 12 indicating they live abroad because of political or social attitudes, this paper conducts a hypothesis test to evaluate the change in proportion.

The null hypothesis (H₀) assumes that the proportion of politically motivated expatriates post-September 11 remains at the historic level of 2%, expressed as H₀: p = 0.02. The alternative hypothesis (H₁) posits that this proportion has increased, formulated as H₁: p > 0.02. Testing these hypotheses involves calculating the sample proportion and the standardized test statistic to evaluate the evidence against the null.

The sample proportion \(\hat{p}\) is derived from the data: \(\hat{p} = \frac{12}{400} = 0.03\). To compute the test statistic, the z-score formula for a proportion is applied:

\[

z = \frac{\hat{p} - p_0}{\sqrt{\frac{p_0 (1 - p_0)}{n}}}

\]

where \(p_0\) is the assumed proportion under the null hypothesis (0.02), and n is the sample size (400). Substituting values:

\[

z = \frac{0.03 - 0.02}{\sqrt{\frac{0.02 \times 0.98}{400}}} = \frac{0.01}{\sqrt{\frac{0.0196}{400}}}

\]

\[

z = \frac{0.01}{\sqrt{0.000049}} = \frac{0.01}{0.007} \approx 1.43

\]

The calculated z-value is approximately 1.43.

Using standard normal distribution tables or statistical software, the p-value associated with \(z = 1.43\) for a one-tailed test is approximately 0.076. Since this p-value exceeds the significance level \(\alpha = 0.05\), the evidence is insufficient to reject the null hypothesis.

Based on the analysis, we fail to reject the null hypothesis at the 5% significance level. Although the observed proportion (3%) is higher than the historic value (2%), this difference is not statistically significant given the data. Therefore, there is no sufficient evidence to conclude that the proportion of politically motivated expatriates has increased since September 11, 2001.

In conclusion, while there appears to be a slight increase in the proportion of expatriates living abroad due to political or social discontent, this change is not statistically significant at the 0.05 level. Further research with a larger sample size or additional data may be necessary to detect more subtle shifts in expatriate motivations over time.

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