# Statistics: The Rate of Household Pets

Statistics: The Rate of Household Pets

Project Description

Describe a problem from your field of interest in which statistical tools may be used to compare two populations on a single variable. State a hypothesis regarding the problem. The variable you select must be a numerical variable (not categorical or ranking). Describe the sampling techniques you are using. The sample size for each of the two groups you are studying has to be at least 30. Use the statistical methods and tools you have learned to analyze your data. Present your results in a well-organized, written report.

Organization of the Report

You will submit a written report of 600-900 words, not including illustrations or bibliography. It must be word-processed using 11 or 12 point font. All graphs and charts must be generated in StatCrunch and included in the electronic document (just like we do in labs). The report must be organized as follows:

Abstract: The body of the paper must be preceded by a 50-150 word abstract that includes the problem statement, the hypothesis that you are testing, the population you are studying, and the main results of your study. This is meant to be a summary of the entire report in one or two paragraphs that people unfamiliar with statistics can understand.

Body: The body of the paper should be organized as follows:

1. Introduction – Describe the problem. Include background information that might be necessary for the reader to understand the problem. Explain why you chose the problem you did and describe your null and alternative hypotheses in terms of the real world problem.

2. Data Collection Methodology – Indicate when, where, and how you collected your data. You MUST randomly sample at least 30 observations per group – comment on how this randomness was achieved. Indicate whether any adjustments made to the raw data (e.g. did you convert percentages to decimals or perform other calculations?).

3. Data Analysis (Note: do ALL calculations in StatCrunch and copy/paste output into report.)

For each of your two samples do the following:

a. Compute the mean, standard deviation, five number summary, and range.

b. Construct a relative frequency table and a frequency histogram.

c. Construct a boxplot and a stem-and-leaf plot.

d. Draw any conclusions that seem appropriate. Include a discussion about the skewness and distribution shape of your data. Be complete and thorough (make sure to discuss all of your graphs and statistics from parts 3a – 3c with the exception of the stem-and-leaf plot). State and support your ideas. You proposed a hypothesis in the introduction – explain whether the data appear to support it. This is the most important part of the Data Analysis! Compare the two groups!

4. Inferential Statistics (Note: do ALL calculations in StatCrunch and copy/paste output into report.)

a. Construct one-mean confidence intervals for each of your two populations. Interpret each of these two confidence intervals.

b. Perform all 6 steps of the two-mean hypothesis test: state the hypothesis, choose a significance level, report the test statistic and p-value, make a decision based on the p-value, and interpret your result. In addition to the StatCrunch output for the test, include the formula for the appropriate test statistic – either paired t or non-pooled two-sample t (can be neatly handwritten).

c. Describe the result of your hypothesis test in a few sentences (in the context of the real world problem) and explain whether the interpretations of your CIs (part 4a) match your test results (part 4b).

5. Conclusions – Detailed discussion that includes your overall conclusions, comments, interpretations, and suggestions. Be sure to include a comment on how the data analysis (part 3d) and inference (part 4c) are aligned. Regarding suggestions, how would you do things differently if you repeated the study? Why do you think you reached the conclusion that you did? Be thorough and use language that people unfamiliar with statistics can understand.

References: Reference websites (with access dates) or documents used as data sources, as well as books or articles referenced in your analysis.

Language and Level

Assume that your reader has a good working knowledge of the ideas covered in MTH 1210. Use correct spelling, complete sentences, and correct grammar. Language skills will not be graded, but well-written papeefrrs inevitably get better grades.