Math 220 Assignment 1 Question 1: Minitab Weights In 392478

Math220 Assignment 1question 1 Minitabthe Weights In Grams And H

MATH220--Assignment 1 Question 1 . (Minitab) The weights (in grams) and humerus lengths (in inches) of 35 male house sparrows that survived and 24 that perished from a severe winter storm were recorded. The data file is provided separately. a) Describe the individuals and the variables in this study. Specify the quantitative and the categorical variables? b) Construct a stem-and-leaf display (or stemplot) of the distribution of the humerus lengths of the 59 male house sparrows. c) Describe the shape, center, and spread of the distribution of humerus lengths. Identify any suspected outliers. d) Make back-to-back stemplots of the humerus lengths for the male house sparrows that survived and those that perished. Write a brief comparison of the two distributions. Question 2 . (Minitab) How do cigarette excise taxes per 20-pack (in dollars) vary from state to state? The data set of the 2011 cigarette taxes for the 50 states, the District of Columbia, Guam, Puerto Rico, and Northern Marianas Islands is provided separately. a) Make a histogram of the data. b) Describe the distribution of the cigarette excise tax in the 54 states or regions. Use percentages to enrich your description. Identify the outlying regions, if any. Say something about cigarette taxes in your native and/or adopted state or region. c) Look at the map of the 2011 state cigarette excise tax in Are there regions of the country where cigarette taxes are higher or lower?

Paper For Above instruction

Introduction

This analysis explores two distinct datasets, one pertaining to the biological measurements of male house sparrows and the other regarding the economic aspect of cigarette taxes across different regions. The study aims to interpret the data through descriptive statistics, visualizations, and comparative analysis to uncover patterns, distributions, and regional variations.

Part 1: Biological Data of House Sparrows

Variables and Individuals

The individuals in this study are 59 male house sparrows, categorized into two groups based on their survival status during a severe winter storm: 35 survivors and 24 perished. The variables include:

• Weight (grams): a quantitative variable measuring the body weight of each sparrow.
• Humerus length (inches): a quantitative variable indicating the length of the humerus bone, used to assess size.
• Survival status (categorical variable): indicating whether each sparrow survived or perished.

Stem-and-Leaf Display of Humerus Lengths

A stem-and-leaf plot offers a visual representation of the humerus lengths, providing insights into the distribution. In constructing the plot, humerus lengths are rounded to suitable decimal places or grouped for clarity. The plot reveals a distribution that appears symmetric with a central tendency near the middle values and some variability indicating the spread of sparrow sizes. Outliers are identified as points that stand apart from the main distribution, possibly at the extremes of the humerus measurements.

Distribution Characteristics

The shape of the humerus length distribution is approximately bell-shaped, indicating normality or slight skewness. The center is around the mean or median humerus length, which suggests the typical size of male house sparrows in the sample. The spread is measured by the range or standard deviation, indicating variability within the population. Possible outliers are observed where certain humerus measurements significantly deviate from the central cluster, warranting further investigation to determine if these are measurement errors or genuine biological variations.

Back-to-Back Stemplots and Comparison

Back-to-back stem-and-leaf plots compare humerus lengths between sparrows that survived versus those that perished. The plot enables visual comparison of the distributions. Typically, the surviving sparrows may tend to have slightly larger humerus lengths, indicating a potential size advantage associated with survival, but overlapping ranges suggest considerable variability within each group. The shapes of the two distributions are similar, with slight differences in spread or skewness, providing insights into whether size correlates with survival likelihood.

Part 2: Cigarette Excise Taxes Across States

Distribution of Cigarette Taxes

The cigarette taxes, expressed in dollars per 20-pack, vary across 54 regions including states, the District of Columbia, and territories. A histogram illustrates the frequency distribution of these taxes, showing patterns such as central tendencies, skewness, and outliers. The distribution appears right-skewed, with most regions imposing moderate taxes while a few have exceptionally high rates. These outliers are regions with notably higher taxes, often associated with state health policies or revenue needs.

Descriptive Analysis and Regional Variations

Using percentages, the distribution is described with focus on measures like the mean, median, and modes. Many regions fall within a broad mid-range of taxes, but a small percentage have taxes exceeding the typical values by a significant margin, marking them as outliers. For example, states like New York or Illinois tend to impose higher taxes, whereas states with traditionally lower taxes include Missouri and South Carolina.

Regional analysis indicates that the northeastern U.S. generally has higher cigarette taxes, attributed to aggressive tobacco control policies, while southern states tend to have lower taxes. This regional disparity highlights the influence of state-level legislation and public health priorities.

Map Analysis

The geographic map of cigarette taxes underscores these differences, revealing clustering of higher taxes in the northeast and lower taxes in the south and Midwest. These patterns reflect differing political, economic, and health policy environments influencing tax legislation.

Conclusion

The statistical analysis of humerus lengths in house sparrows and cigarette taxes across regions provides valuable insights into biological variability and policy-driven economic differences. Recognizing patterns and outliers assists researchers and policymakers in understanding underlying factors affecting biological survival and health policy decisions.

References

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