Is there an association between hair color and body type?
College Algebra (MindTap Course List)
12th Edition
ISBN:9781305652231
Author:R. David Gustafson, Jeff Hughes
Publisher:R. David Gustafson, Jeff Hughes
Chapter8: Sequences, Series, And Probability
Section8.7: Probability
Problem 58E: What is meant by the sample space of an experiment?
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Is there an association between hair color and body type? The table below shows the results of a researcher's observations of randomly selected people.
Frequencies of Hair Colors for Various Body Types
Blonde | Brunette | Red Head | |
---|---|---|---|
Short and Slender | 80 | 84 | 52 |
Short and Pudgy | 91 | 105 | 72 |
Tall and Slender | 59 | 96 | 68 |
Tall and Heavy | 60 | 109 | 75 |
What can be concluded at the αα = 0.05 significance level?
- What is the correct statistical test to use?
- Paired t-test
- Goodness-of-Fit
- Homogeneity
- Independence
- What are the null and alternative hypotheses?
H0:H0:- The distribution of hair color is the same for each body type.
- The distribution of hair color is not the same for each body type.
- Hair color and body type are dependent.
- Hair color and body type are independent.
H1:H1:- Hair color and body type are dependent.
- The distribution of hair color is not the same for each body type.
- Hair color and body type are independent.
- The distribution of hair color is the same for each body type.
- The test-statistic for this data = (Please show your answer to three decimal places.)
- The p-value for this sample = (Please show your answer to four decimal places.)
- The p-value is Select an answer greater than less than (or equal to) αα
- Based on this, we should
- fail to reject the null
- accept the null
- reject the null
- Thus, the final conclusion is...
- There is insufficient evidence to conclude that hair color and body type are dependent.
- There is insufficient evidence to conclude that the distribution of hair color is not the same for each body type.
- There is sufficient evidence to conclude that the distribution of hair color is not the same for each body type.
- There is sufficient evidence to conclude that hair color and body type are independent.
- There is sufficient evidence to conclude that hair color and body type are dependent.
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