You Want To Rent An Unfurnished One-Bedroom Apartment

You Want To Rent An Unfurnished One Bedroomapartmentfor

You want to rent an unfurnished one-bedroom apartment for next semester. The mean monthly rent for a random sample of 10 apartments advertised in the local newspaper is $640. Assume that the standard deviation is $90. Find a 95% confidence interval for the mean monthly rent of an apartment.

Paper For Above instruction

The task involves calculating a 95% confidence interval for the mean monthly rent of an unfurnished one-bedroom apartment based on a sample. Given the sample mean of $640, sample size of 10, and population standard deviation of $90, we apply the principles of inferential statistics to estimate the range within which the true mean rent likely falls.

First, understanding the concept of a confidence interval is essential. A confidence interval provides a range of values, derived from a sample, that is likely to contain the true population parameter with a certain level of confidence—in this case, 95%. The formula for the confidence interval when the population standard deviation is known and the sample size is small (n

CI = x̄ ± z*(σ/√n)

Where:

  • x̄ is the sample mean, which is $640
  • σ is the population standard deviation, which is $90
  • n is the sample size, which is 10
  • z* is the z-value corresponding to the desired confidence level, which for 95% is approximately 1.96

Calculating the standard error (SE):

SE = σ / √n = 90 / √10 ≈ 90 / 3.162 ≈ 28.46

Next, multiply the standard error by the z-value to find the margin of error (ME):

ME = z* × SE = 1.96 × 28.46 ≈ 55.77

Finally, establish the confidence interval:

Lower bound: 640 - 55.77 ≈ $584.23

Upper bound: 640 + 55.77 ≈ $695.77

Therefore, with 95% confidence, the true mean monthly rent for unfurnished one-bedroom apartments in the area is approximately between $584.23 and $695.77. This interval provides a useful estimate for prospective renters and property managers to understand typical rental prices within this confidence level.

References

  • Devore, J. L. (2015). Probability and Statistics for Engineering and the Sciences. Brooks/Cole, Cengage Learning.
  • Lehmann, E. L., & Casella, G. (2003). Theory of Point Estimation. Springer Science & Business Media.
  • Moore, D. S., McCabe, G. P., & Craig, B. A. (2017). Introduction to the Practice of Statistics. W.H. Freeman.
  • Walpole, R. E., Myers, R. H., Myers, S. L., & Ye, K. (2012). Probability and Statistics for Engineers and Scientists. Pearson Education.
  • Ross, S. M. (2014). Introduction to Probability and Statistics for Engineers and Scientists. Academic Press.
  • Agresti, A., & Franklin, C. (2013). Statistics: The Art and Science of Learning from Data. Pearson.
  • Freeman, J. (2018). Business Statistics: A Decision-Making Approach. Routledge.
  • Myers, R. H., & Well, A. D. (2003). Research Design and Statistical Analysis. Routledge.
  • Field, A. (2013). Discovering Statistics Using IBM SPSS Statistics. Sage Publications.
  • Gelman, A., Carlin, J. B., Stern, H. S., Dunson, D. B., Vehtari, A., & Rubin, D. B. (2013). Bayesian Data Analysis. Chapman and Hall/CRC.

Related Assignments