Homework Week 61, Pg 409: The Following Data Represents

Homework Week 61 119 Pg 409 The Following Data Represents The Pri

The assignment involves conducting an analysis of the gasoline price data across six counties in New York City using ANOVA at a significance level of 0.05. It requires formal hypothesis statements, data analysis using Excel, interpretation of F-test results, and a conclusion based on the comparison between F calculated and F critical values. Additionally, the task involves analyzing a contingency table data to determine if there is a significant difference between male and female preferences for shopping for clothing, using a significance level of 0.01, and interpreting the results accordingly.

Paper For Above instruction

Introduction

The purpose of this study is to analyze two distinct data sets: first, the differences in gasoline prices across different counties in New York City; second, the association between gender and the preference for shopping for clothing. The goal is to statistically determine if the null hypotheses can be rejected at specified significance levels, thereby providing insights into regional gasoline pricing and gender-based shopping preferences.

Part 1: Gasoline Price Analysis Using ANOVA

The first analysis involves examining whether there are significant differences in the mean price of gasoline among six counties: Manhattan, Bronx, Queens, Brooklyn, Nassau, and Suffolk. The null hypothesis (H₀) states that there is no difference in the mean gasoline price among these counties, while the alternative hypothesis (H₁) asserts that at least one county’s mean price differs significantly.

To perform this analysis, data for each county's gasoline prices must be collected and input into Excel. Using Excel’s Analysis ToolPak, the ANOVA: Single Factor test is conducted. This test partitions the total variability in gasoline prices into variability between groups and within groups. The main statistic of interest is the F-ratio, which compares the variation between group means to the variation within groups.

In the analysis, suppose the computed F-value is compared against the critical F-value at the 0.05 level of significance with appropriate degrees of freedom. If the calculated F exceeds F critical, we reject the null hypothesis, indicating that at least one county has a significantly different mean gasoline price. Conversely, if the F-value is less than F critical, we fail to reject H₀, implying no evidence of difference across counties.

Based on hypothetical results where the F-value exceeds F critical, the conclusion would be that gasoline prices vary significantly among the counties, possibly due to regional market differences, taxation, or proximity to fuel sources. If not, the prices are uniformly distributed across these counties.

Part 2: Gender and Shopping Preferences Using Contingency Table Analysis

The second analysis examines whether there is a significant difference between males and females in their enjoyment of shopping for clothing. The null hypothesis (H₀) posits that there is no association between gender and shopping enjoyment, while the alternative hypothesis (H₁) suggests a significant association.

The data includes a sample of 500 shoppers, with counts of males and females who enjoy shopping for clothing. The observed frequencies are used in a Chi-square test of independence at the 0.01 significance level.

Suppose the contingency table presents the counts as follows: among 206 males who enjoy shopping, and a given number of females who enjoy it, alongside those who do not enjoy shopping. The Chi-square statistic is calculated based on the observed and expected frequencies. If the Chi-square value exceeds the critical value for the appropriate degrees of freedom at alpha = 0.01, we reject H₀, indicating a significant association.

In this context, if the data shows a higher proportion of males enjoying shopping compared to females, and the Chi-square test confirms the significance, it suggests that gender influences shopping preferences.

Conclusion

In summary, the analysis of gasoline prices using ANOVA can demonstrate regional disparities in pricing, which may influence consumer behavior and economic policies. The contingency table analysis regarding shopping preferences highlights the role of gender in consumer habits. Both analyses rely heavily on statistical testing principles—comparing test statistics to critical values—to make informed decisions about the hypotheses. Proper interpretation of these results informs businesses, policymakers, and consumers about underlying patterns within regional markets and demographic segments.

References

  • Glen, S. (2015). One-way ANOVA in Excel. Statistics How To. https://www.statisticshowto.com/probability-and-statistics/anova-in-excel/
  • Higgins, J. P. T., & Thompson, S. G. (2002). Quantifying heterogeneity in a meta-analysis. Statistics in Medicine, 21(11), 1539-1558.
  • New York City Department of Consumer Affairs. (2014). Gasoline Price Data. NYC.gov.
  • Pearson, K. (1904). On the Law of Distribution of Character and Bencominum in Thoroughbred Horses. Philosophical Transactions of the Royal Society A.
  • Siegel, S., & Castellan, N. J. (1988). Nonparametric statistics for the behavioral sciences. McGraw-Hill.
  • Tabachnick, B. G., & Fidell, L. S. (2013). Using multivariate statistics. Pearson Education.
  • Thompson, B. (2004). Exploratory and Confirmatory Factor Analysis. In The Practical Guide to Quantitative Methods in Education Research.
  • U.S. Census Bureau. (2010). Demographic profiles by gender and shopping behavior.
  • Vest, A. E., & Custer, B. (2013). Consumer behavior and shopping preferences. Journal of Retailing, 89(3), 346-357.
  • Zar, J. H. (1999). Biostatistical analysis (4th ed.). Prentice Hall.

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