STAT 280 Applied Stats (001) SU1 2024 Week 6 Discussion 6 | Confidence Intervals

Review the assigned reading to prepare for this discussion. 

For the Real Estate Evaluation Project, you have been working solely with a random sample of a data set of property prices. You found the mean price of homes, townhomes, and units of your sample. How confident can you be that the sample means are actually representative of the true mean of the property prices of all homes, townhomes, and units in the region represented by the data? In this discussion, you will use your data from Part 1 of the Real Estate Evaluation Project to explore the meaning of a confidence interval. In preparation for this discussion, it is imperative that you complete the assigned reading prior to posting, taking good notes and working through the examples in the text (Chapter 8, “Confidence Intervals”).

For our purposes, assume that the property prices of homes are normally distributed (this is a necessary condition for confidence intervals). The population standard deviation of the price of homes is known and is given by σ=$704,500.

Use your data set (TAB 2) from Part 1 of the Real Estate Evaluation Project to complete the table [DOWNLOAD]. For the sample size of n = 10, find the mean of the first 10 home prices from your random sample. For the sample size of n = 30, find the mean of the next 30 home prices from your random sample (not including the first ten home prices). For the sample size of n = 50, find the mean of the next 50 home prices from your random sample, which does not include any of the home prices used prior. For the sample size of n = 100, find the mean of the next 100 home prices from your random sample, which does not include any of the home prices used prior, if possible. Depending on how many homes were in your random sample, you may have to include some already-used property prices. Use technology, either Google sheets or another tool of your choice, to find the mean of the different samples.

1. Complete the table [DOWNLOAD], and share it with your peers as a part of your initial post. Embed your table directly into your discussion post on the discussion board.
• Instructions for Embedding Pictures Into a Discussion Post [DOWNLOAD]
2. Interpret the confidence interval in the context of the problem for the n = 100 case. In Introduction to Statistics by Barbara Illowsky & Susan Dean, see the introduction of Chapter 8, as well as section 8.1, “A Single Population Mean Using the Normal Distribution” for guidance on the interpretation of a confidence interval.
• How does sample size appear to affect the sample mean? How does sample size affect the 95% confidence interval, if at all.
3. Compare your 95% confidence interval for n = 100 with that of your peers. Additionally, comment on the role that sample size plays in statistics in general. What effect would the inclusion of sample size in a report that provides statistics have on an audience? Explain.

Requirements

• Initial posts: 150-250 words