Explain how you might see the implications of this workdifferently

Summary Table for Predicted Population Mean of Family Income(In Constant Dollars)estimated by sample sizes of100and400at confidence levels of95%and90%respectively

Sample Size

Confidence Level

Sample Mean Confidence Interval

100

95% 52,642.04 8,859.60

100

90% 52,642.04 7,410.71

400

95% 46,934.32 4,227.77

400

90% 46,934.32 3,545.27

(IBM Corp., 2020-General Social Survey Dataset C)

The CLs and CIs will help predict the population family income mean. Sample size100 at 95%CLshows that there is a population prediction family income mean between43,782.44 and 61,501.64(This range is a result of52,642.04 + 8,859.60 and 52,642.04 - 8,859.60)---the range is the sample mean the margin of error (Frankfort-Nachmias et al., 2020). Now, for sample size100 at 90% CL,there is a population prediction family income mean between45,231.33 and 60,052.75. Please note these numbers are the upper and lower bounds at the 95% and 90% marks for sample size 100. If we increase the sample size to400 at 95% CL, the population prediction family income mean is between42,706.55 and 51,162.09. Next is the population prediction family income mean of sample size400 at 90%CLis between43,389.05 and 50,479.59(IBM Corp., 2020).

I notice that the confidence level has a direct correlation to the width of the confidence interval. When the confidence level is higher at 95%, the width is more significant in both sample sizes than 90%. Frankfort-Nachmias et al. (2020) state that researchers are looking to make an accurate prediction that is the most accurate representation of the larger population. Even though 90% CLs in both sample sizes have smaller widths, it may not be the most accurate representation with a 10% chance of error. Also, the sample size of 100 has a much higher margin of error (Walden University, 2021)than the sample size of 400. So it seems it is not about changing the confidence level but increasing the sample size so there will be a larger sample size to represent the larger population. Therefore, we only have a 5% chance of error instead of a 10% chance of error by keeping the CL at 95% to produce a more accurate depiction of the population mean (Walden University, 2021).

Confidence intervals are a great tool to help look at the range of intervals instead of just looking at 1 sample or a point estimate (Walden University, 2021). A point estimate cannot be an accurate representation of the larger population. There will never be exact numbers in the population, but we can have a good sample size at 95% confidence level to get a good idea of the representation of the population. If we bring this back to a policy perspective and we are looking at amending a homebuying program or looking at an affordable housing program, and we want an idea of families' average income, then we would want the most accurate numbers and a larger sample size best depicts this at 95%CL to get the best CI to represent the average population income. This would have so many implications in social change---are we trying to help more families or just a specific group? Just a thought. I would love to hear more from the group about what you all think about this data's social change and policy implications. Families' Incomes is such a hot topic and a sensitive topic regarding qualifications for government policies and programs. The other sensitive topic that comes to mind is taxes. Confidence Levels and Confidence Intervals must be used at the most point of accuracy when developing tax laws for families' incomes in each state and federal government. I think all families want to make sure they are in the appropriate categories. *Dr. Yu, if you need my outputs from SPSS, let me know, and I will make another post with the screenshots.