Math 220 Assignment 1 Question 1: Minitab Weights In Grams

Math220 Assignment 1question 1 Minitabthe Weights In Grams And H

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.

Paper For Above instruction

The study focusing on the physical characteristics of male house sparrows during a severe winter storm provides valuable insights into how environmental stressors affect avian populations. The individuals in this study are 59 male house sparrows, a common bird species, with 35 of these individuals having survived the winter storm, while 24 perished. The variables recorded include two types: quantitative variables, namely the weight in grams and humerus length in inches, and a categorical variable indicating survival status (survived or perished).

Understanding the individuals involves recognizing each sparrow as an individual data point with specific measurements, while the variables—weight, humerus length, and survival status—capture the characteristics that might influence or reflect the bird's response to environmental adversity. The quantitative variables, weight and humerus length, are continuous measurements that can be analyzed for distribution patterns, centers, and variability. The categorical variable, survival status, allows for subgroup analysis and comparison between the two groups using graphical representations such as back-to-back stemplots.

Constructing a stem-and-leaf display of humerus lengths entails organizing the data to visualize the distribution effectively. In Minitab, this involves choosing GRAPH > Stem-and-leaf, selecting the humerus length variable, and ensuring outliers are not trimmed to observe the full spread. The resulting display reveals the distribution's shape and potential outliers. Typically, such a stemplot may show a roughly symmetrical distribution with some outliers at either tail, indicating variable biological responses among the sparrows.

Descriptive analysis of the distribution focuses on the pattern, central tendency, and variability. The shape could be roughly symmetric or skewed, depending on how the data cluster around the center. The center can be approximated using the median or mean humerus length, while the spread can be measured by the interquartile range or range. Identification of outliers—data points markedly distant from the main distribution—is essential, as they may influence the results or indicate biological anomalies.

To compare the humerus lengths of sparrows that survived versus those that perished, back-to-back stemplots provide a side-by-side visualization. In Minitab, this involves selecting the humerus length variable and specifying the status-coded variable ('0' for perished and '1' for survived). The resulting separate stemplots reveal differences or similarities in the distributions—for example, whether surviving sparrows tend to have longer humerus lengths or if the distributions are similar, indicating no apparent size difference between the two groups.

Such graphical comparisons help elucidate whether physical characteristics like humerus length correlate with survival, which could be linked to factors such as flight capability or energy reserves. Further statistical tests, like t-tests or non-parametric equivalents, could confirm whether observed differences are statistically significant.

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