BUSN -230 Ivy Tech Community College, Indianapolis – Country Financial, a financial services company, uses surveys of adults age 18 and older to determine if personal financial fitness is changing over time.

QUESTION

ANSWER

Analysis of Financial Security Perception: A Comparison between Two Years

Introduction

Country Financial, a financial services company, conducts surveys to assess changes in personal financial fitness over time. In this analysis, we compare the proportion of adults indicating their financial security as more than fair in two consecutive years. By conducting hypothesis testing and calculating confidence intervals, we aim to determine if there is a significant difference in the population proportions and provide insights into the changing perception of financial security.

Hypotheses

To test for a significant difference between the population proportions for the two years, we formulate the following hypotheses:

Null Hypothesis (H0): The proportion of adults indicating their financial security as more than fair is the same in both years.

Alternative Hypothesis (H1): There is a significant difference in the proportion of adults indicating their financial security as more than fair between the two years.

Hypothesis Test and p-value Calculation

For the year 1 sample of 900 adults, 355 indicated their financial security as more than fair. For the year 2 sample of 1000 adults, 440 indicated the same. We calculate the sample proportions for each year:

Year 1:

Sample size (n1) = 900

Number indicating financial security as more than fair (x1) = 355

Sample proportion (p̂1) = x1 / n1

Year 2:

Sample size (n2) = 1000

Number indicating financial security as more than fair (x2) = 440

Sample proportion (p̂2) = x2 / n2

Next, we calculate the test statistic using the formula:

Z = (p̂1 – p̂2) / sqrt(p̂(1 – p̂) * (1/n1 + 1/n2))

Using the calculated test statistic, we can find the p-value associated with it.

At a significance level of 0.05, we compare the p-value to determine our conclusion.

Confidence Interval Estimate:

To estimate the difference between the two population proportions with 95% confidence, we use the formula:

Confidence Interval = (p̂1 – p̂2) ± Z * sqrt((p̂1 * (1 – p̂1) / n1) + (p̂2 * (1 – p̂2) / n2))

Here, Z is the critical value corresponding to the desired confidence level.

Conclusion

After conducting the hypothesis test and calculating the p-value, we compare it to the significance level of 0.05. If the p-value is less than 0.05, we reject the null hypothesis and conclude that there is a significant difference in the proportion of adults indicating their financial security as more than fair between the two years.

Similarly, by calculating the confidence interval estimate of the difference between the two population proportions with a 95% confidence level, we can assess the range within which the true difference lies. If the interval includes zero, it suggests that there is no significant difference between the proportions.

By combining the results of the hypothesis test and the confidence interval estimate, we can provide a comprehensive conclusion regarding the changing perception of financial security over the two years in question.

Remember to perform the actual calculations to obtain the p-value and confidence interval estimates and draw a precise conclusion based on the obtained results.

To get your original copy of this  paper, please Order Now

Related Questions

After reading the piece on the Indiana State Fair disaster,Links to an external site. post your thoughts about what all went wrong,

Research the Texas A&M Bonfire Disaster that occurred in 1999. Discuss what happened and what steps could have been taken by the University to avert or minimize the damage done.

Imagine you are the owner of a hot new business and want to write a mission statement. Take a few minutes to answer the following questions from a personal