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 88 97 48 Short and Pudgy 88 102 60 Tall and Slender 53 91 69 Tall and Heavy 58 119 76 What can be concluded at the αα = 0.01 significance level? What is the correct statistical test to use? Independence Homogeneity Goodness-of-Fit Paired t-test What are the null and alternative hypotheses? H0:H0: The distribution of hair color is not the same for each body type. Hair color and body type are dependent. The distribution of hair color is the same for each body type. Hair color and body type are independent. H1:H1: 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. Hair color and body type are dependent. 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 Based on this, we should fail to reject the null reject the null accept the null Thus, the final conclusion is... 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 hair color and body type are dependent. There is sufficient evidence to conclude that hair color and body type are independent. There is insufficient evidence to conclude that hair color and body type are dependent. There is sufficient evidence to conclude that the distribution of hair color is not the same for each body type.

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018

18th Edition

ISBN:9780079039897

Author:Carter

Publisher:Carter

Chapter10: Statistics

Section10.4: Distributions Of Data

Problem 19PFA

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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	88	97	48
Short and Pudgy	88	102	60
Tall and Slender	53	91	69
Tall and Heavy	58	119	76

What can be concluded at the αα = 0.01 significance level?

What is the correct statistical test to use?
- Independence
- Homogeneity
- Goodness-of-Fit
- Paired t-test
What are the null and alternative hypotheses?
H0:H0:
- The distribution of hair color is not the same for each body type.
- Hair color and body type are dependent.
- The distribution of hair color is the same for each body type.
- Hair color and body type are independent.
H1:H1:
- 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.
- Hair color and body type are dependent.
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
Based on this, we should
- fail to reject the null
- reject the null
- accept the null
Thus, the final conclusion is...
- 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 hair color and body type are dependent.
- There is sufficient evidence to conclude that hair color and body type are independent.
- There is insufficient evidence to conclude that hair color and body type are dependent.
- There is sufficient evidence to conclude that the distribution of hair color is not the same for each body type.

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