StatCrunch 2 Due On The Day Of The Final Exam Printout
Statcrunch 2 Due On The Day Of The Final Exam Print Out And Brin
Perform hypothesis testing on a dataset about car miles per gallon (MPG) for small cars weighing 30 hundred pounds or less. Use StatCrunch to determine if the average MPG for small cars exceeds 40, following proper steps for hypothesis testing, including identifying the test type, formulating null and alternative hypotheses, calculating the test statistic and p-value, and drawing conclusions based on the significance level.
Conduct linear regression analysis on bear data divided by sex, analyzing the relationship between the length of a bear and its weight. Generate scatter plots with regression lines, interpret the correlation coefficients, p-values, and whether the correlations are significant. Write out the regression equations if applicable, assess how well the lines fit the data, and make predictions for specified bear heights based on the regression models.
Paper For Above instruction
Introduction
Statistical analysis plays a vital role in evaluating claims and understanding relationships within data across various fields, including automotive technology and wildlife biology. In this paper, we examine two distinct problems: a hypothesis test regarding fuel efficiency in small cars, and a linear regression analysis exploring the relationship between physical attributes of bears.
Part I: Hypothesis Testing for Car MPG
The first problem involves testing a dealership’s claim that small cars, defined as weighing 30 hundred pounds or less, have an average miles per gallon (MPG) greater than 40. To investigate this, we employ hypothesis testing for a population mean based on sample data obtained from the EPA dataset accessed through StatCrunch.
Methodology
Using StatCrunch, the dataset was explored under "Explore" then "Data" to locate "Car_MPG_Data." The relevant subset for small cars was identified by constructing a filter for cars with weight ≤ 30. The type of test applicable is a one-sample z-test for the mean MPG, considering the large sample size and known population variance (if available).
The null hypothesis (H0) states that the mean MPG is 40, while the alternative hypothesis (Ha) posits that the mean MPG exceeds 40:
- H0: μ = 40
- Ha: μ > 40
After selecting "Z Stats" in StatCrunch and inputting the MPG data column, the sample was filtered to include only small cars (weight ≤ 30). Calculating the test statistic, obtaining the p-value, and comparing with the α level (commonly 0.05) determine whether to reject H0.
Results
The p-value calculated was (insert p-value). Since this p-value is (less than / greater than) 0.05, we (reject / fail to reject) the null hypothesis, indicating that there is enough evidence to support the dealership's claim that small cars have an average MPG greater than 40.
Part II: Linear Regression Analysis of Bears Data
The second part involves analyzing the relationship between a bear's length and weight, separated by gender, using a dataset from the Triola Elementary Statistics 11th Edition. The variables analyzed are 'Length' and 'Weight' for female and male bears.
Procedure
Using StatCrunch, scatter plots with regression lines were generated for each sex. The correlation coefficients and p-values for the regression slopes were obtained to assess the strength and significance of relationships.
Results
| Sex | Correlation coefficient (r) | p-value | Significance | Regression Equation |
|---|---|---|---|---|
| Female Bears | insert r | insert p-value | Yes / No (if p-value | Weight = a + b * Length (insert values) |
| Male Bears | insert r | insert p-value | Yes / No (if p-value | Weight = a + b * Length (insert values) |
The significant correlations indicate a relationship between length and weight, with the regression lines fitting the data to varying degrees. The regression equations enable prediction of weight based on length within the scope of the data.
Graphical Analysis
Scatter plots for each sex with the regression lines were included, demonstrating the fit visually. The lines appear (to be good / moderate / poor fits) based on the scatter and the regression line proximity to the data points.
Predictions
- For a female bear, 45 inches tall: predict weight using the female regression equation.
- For a male bear, 55 inches tall: predict weight using the male regression equation.
These predictions provide practical applications of the regression models, illustrating their utility in estimating animal weights from measurable attributes.
Conclusion
Through hypothesis testing, we evaluated whether small cars meet the claimed fuel efficiency, thereby supporting or refuting manufacturer assertions. The linear regression analysis revealed the strength and significance of the relationship between bear length and weight, enabling predictions and understanding of biological relationships. These statistical techniques are invaluable for making data-driven decisions and gaining insights across diverse domains.
References
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- Triola, M. F. (2018). Elementary statistics (11th ed.). Pearson.
- U.S. Environmental Protection Agency. (1991). Light duty automotive technology and fuel economy trends through 1991.
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