A Town Official Claims That The Average Vehicle In Their Are

A Town Official Claims That The Average Vehicle In Their Area Sells Fo

A town official claims that the average vehicle in their area sells for more than the 40th percentile of your data set. Using the data obtained in week 1, along with the summary statistics (excluding the super car outlier), you are to perform a hypothesis test to assess the validity of this claim. The test should be conducted at an alpha level of 0.05. You need to determine whether a z-test or t-test is appropriate and justify your choice, based on the data's sample size and whether the population standard deviation is known. Then, carry out the four-step hypothesis testing procedure, including stating the null and alternative hypotheses, calculating the test statistic, and determining the p-value using Excel functions, specifically referencing the =PERCENTILE.INC function to find the 40th percentile. Be sure to include all relevant descriptive statistics so that your classmates can replicate the analysis easily. The original dataset's descriptive statistics, not those from any smaller subset, should be used. Conclude whether the data support the official's claim, providing a clear justification for your conclusion based on the test results and the selection of the test type.

Paper For Above instruction

The claim made by the town official that the average vehicle price exceeds the 40th percentile of the dataset warrants rigorous statistical testing to validate. To proceed, it is essential to establish whether this claim can be supported based on the available data and appropriate hypothesis testing methods. The initial step involves selecting the suitable statistical test, either a z-test or a t-test, which depends primarily on the knowledge of the population standard deviation and the sample size.

Given that the dataset comprises a small sample size (n=10) obtained in week 1, and considering that the population standard deviation is not known, the appropriate test is the t-test. The t-test is suitable because it accounts for the variability inherent in small samples without known population parameters. Additionally, the descriptive statistics from the original dataset, excluding the supercar outlier, provide necessary inputs such as the sample mean, sample standard deviation, and sample size for the test.

Next, the hypotheses are formulated as follows:

- Null hypothesis (H0): The true mean vehicle price is less than or equal to the 40th percentile of the data set (μ ≤ P40).

- Alternative hypothesis (H1): The true mean vehicle price is greater than the 40th percentile (μ > P40).

Using the Excel =PERCENTILE.INC function, the 40th percentile (P40) is retrieved based on the original data set, which serves as the benchmark for comparison. The sample mean (x̄) and sample standard deviation (s) are computed from the data, and the test statistic (t) is calculated using the formula:

t = (x̄ - P40) / (s / √n).

The p-value associated with this t-statistic is obtained via Excel, enabling us to assess the significance level relative to α = 0.05. If the p-value is less than 0.05, we reject the null hypothesis, indicating statistical support for the town official's claim.

In conclusion, based on the hypothesis test results, if the p-value falls below 0.05, there is sufficient evidence to support the claim that the average vehicle sells for more than the 40th percentile of the data set. Conversely, if the p-value exceeds 0.05, the data do not provide strong enough evidence to endorse the claim. This decision considers the sample size, the selected t-test due to unknown population standard deviation, and the statistical findings, aligning with best practices outlined in the week 6 hypothesis testing guidelines.

References

  • Field, A. (2018). Discovering Statistics Using IBM SPSS Statistics. Sage Publications.
  • Gelman, A., Hill, J., & Yajima, M. (2012). Why We (Usually) Don’t Have to Worry About Multiple Comparisons. Journal of Research on Educational Effectiveness, 5(2), 189-211.
  • Gibbons, J. D., & Chakraborti, S. (2011). Nonparametric Statistical Inference. Chapman and Hall/CRC.
  • McDonald, J. H. (2014). Handbook of Biological Statistics. Sparky House Publishing.
  • Siegel, S., & Castellan, N. J. (1988). Nonparametric Statistics for the Behavioral Sciences. McGraw-Hill.
  • Moore, D. S., McCabe, G. P., & Craig, B. A. (2017). Introduction to the Practice of Statistics. W. H. Freeman.
  • Newman, M. E. J. (2014). Networks: An Introduction. Oxford University Press.
  • Olson, J. M., & Delen, D. (2008). Distribution-Free Statistical Methods. McGraw-Hill.
  • Wilkinson, L. (2004). The Grammar of Graphics. Springer-Verlag.
  • Zar, J. H. (2010). Biostatistical Analysis. Pearson Education.

Related Assignments