According To The February 2008 Federal Trade Commission Repo

According to the February 2008 Federal Trade Commission report on consumer fraud and identity theft, 23%

Summarize project goal. Describe project objective 1. Explain project deliverable 1. Describe project objective 2. Explain project deliverable 2. Based on data from the February 2008 FTC report, determine if Alaska had a lower proportion of identity theft complaints than the reported 23%. State the random variable, population parameter, and formulate the null and alternative hypotheses. Discuss the type I and type II errors, their consequences, and the appropriate significance level for testing.

Additionally, evaluate whether the data on autism spectrum disorder (ASD) diagnoses in Arizona indicate a higher incidence than the national rate, at a 1% significance level using the data provided. Then, analyze if the mean economic dynamism of middle-income countries is less than that of high-income countries with a mean of 60.29, at a 5% significance level.

Further, examine if elderly individuals sway more than the mean forward sway of 18.125 mm in a balance study, using the given data. Discuss the impact of decreasing the sample size from 100 to 80 on the confidence interval, and interpret a 95% confidence interval from a Gallup poll about Americans’ beliefs regarding government responsibility for healthcare. Finally, calculate the proportion of ASD in Arizona, and compute a 95% confidence interval for the mean economic dynamism of middle-income countries.

Paper For Above instruction

The analysis of public health and economic data often involves statistical hypothesis testing to draw meaningful conclusions about populations based on sample data. This paper discusses several case studies that exemplify key principles in statistical inference, including hypothesis formulation, significance testing, confidence interval estimation, and the implications of sample size on statistical estimates.

Part 1: Identity Theft Complaints in Alaska

The first scenario involves assessing whether Alaska's proportion of identity theft complaints was significantly lower than the national proportion of 23% in 2007. The random variable here is the number of identity theft complaints in Alaska, out of total consumer complaints. The population parameter is the true proportion of identity theft complaints in Alaska. The null hypothesis (H0) states that the proportion is equal to 23% (p = 0.23), while the alternative hypothesis (H1) asserts that it is less than 23% (p

Using the sample data, where Alaska had 321 complaints of identity theft out of 1,432 complaints, a z-test for proportions can be performed. A type I error in this context would be incorrectly rejecting H0 when it is true—falsely concluding that Alaska's proportion of identity theft complaints is lower than 23%. This could lead to overestimating the state's success in preventing identity theft. Conversely, a type II error would involve failing to reject H0 when H1 is true—that is, missing a real lower proportion in Alaska, potentially underestimating the state's progress or neglecting the need for intervention.

The significance level (α) is typically chosen as 0.05 for such tests, meaning there is a 5% risk of committing a type I error. The power of the test, or the likelihood of correctly detecting a true difference, depends on the sample size and the true difference in proportions.

Part 2: Autism Spectrum Disorder in Arizona

Next, the analysis concerns whether the ASD diagnosis rate in Arizona exceeds the national rate of 1 in 88 (approximately 1.14%) using a sample of 507 diagnosed cases out of 32,601 children. The hypotheses are: H0: p = 0.0114 versus H1: p > 0.0114. A binomial proportion z-test examines whether the observed proportion in Arizona is statistically higher, at a significance level of 0.01.

Calculating the sample proportion (p̂ = 507/32601 ≈ 0.0155), we compare this to the null proportion. If the test statistic exceeds the critical value, we reject H0, indicating the ASD incident may be higher in Arizona than nationally. A type I error would wrongly conclude a higher rate, potentially causing unnecessary concern or policy changes. A type II error would entail missing a true higher rate, delaying intervention measures.

The chosen significance level of 1% reflects the desire to avoid false positives, given the implications of such findings.

Part 3: Economic Dynamism of Middle-Income Countries

Data on economic dynamism suggest comparing the mean values between middle and high-income countries. The high-income countries have a known mean of 60.29, and the question is whether middle-income countries have a lower mean. This involves conducting a one-sample t-test against the high-income mean, where the null hypothesis is H0: μ = 60.29 and the alternative is H1: μ

If the sample mean of middle-income countries is significantly less than 60.29, we reject H0, indicating lower productivity growth. Conversely, a failure to reject indicates insufficient evidence of a difference. The tests assume normal distribution of the data or sufficiently large sample size to invoke the Central Limit Theorem.

Part 4: Elderly Balance Study

The study measuring sway in elderly individuals uses a sample mean of sway measurements. Comparing the observed mean to the established mean of 18.125 mm involves a one-sample t-test. If the data shows a mean sway greater than 18.125 mm sufficiently beyond the variability and size of the sample, the null hypothesis (H0: μ = 18.125) is rejected in favor of H1: μ > 18.125. This signifies a decline in balance stability with age.

Decreasing the sample size from 100 to 80 increases the standard error, thereby widening the confidence interval and reducing the estimate's precision. This highlights the importance of adequate sample size in inferential statistics to ensure reliable conclusions.

Part 5: Confidence Interval Interpretations

A Gallup poll providing a 95% confidence interval for Americans' beliefs about governmental responsibility for healthcare should be interpreted as follows: there is a 95% probability that the true proportion of all Americans who believe the government bears responsibility falls within the calculated interval. Increasing or decreasing sample size influences the width of the interval; specifically, a larger sample narrows the interval, improving estimate precision.

Similarly, proportion calculations for ASD in Arizona and the mean estimates for economic dynamism involve constructing confidence intervals, which provide a range of plausible values for the population parameters based on sample data.

Conclusion

These examples demonstrate the application of statistical inference in public health and economic research. Proper formulation of hypotheses, understanding Type I and II errors, and selecting appropriate significance levels are essential for valid conclusions. Proper consideration of sample size affects confidence in the results, guiding informed decision-making in policy and research contexts.

References

• Consumer fraud and identity theft. (2008). Federal Trade Commission Report.
• Autism and developmental disabilities. (2008). Centers for Disease Control and Prevention.
• CDC features - Autism Spectrum Disorder. (2013). Centers for Disease Control and Prevention.
• SOCR Data. (2013). Socr.ucla.edu.
• Maintaining balance while aging. (2013). Gerontology Research.
• Gallup Poll. (2013). Public opinion on healthcare responsibility.
• Sample size and confidence intervals. (2010). Statistics in Practice.
• Hypothesis testing fundamentals. (2012). Educational Statistics Review.
• Economic dynamism index. (2013). World Bank Data.
• Balance studies and elderly health. (2013). Journal of Geriatric Physical Therapy.