Question

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

BlondeBrunetteRed Head

Short and Slender849958

Short and Pudgy7810272

Tall and Slender5010471

Tall and Heavy539361

What can be concluded at the αα = 0.10 significance level?

What is the correct statistical test to use?

Goodness-of-Fit

Paired t-test

Homogeneity

Independence

What are the null and alternative hypotheses?
H0:H0:

The distribution of hair color is not the same for each body type.

The distribution of hair color is 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.

The distribution of hair color is the same for each body type.

Hair color and body type are independent.

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 less than (or equal to) greater than  αα

Based on this, we should

reject the null

fail to reject the null

accept the null

Thus, the final conclusion is...

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 sufficient evidence to conclude that the distribution of hair color is not the same for each body type.

There is insufficient evidence to conclude that the distribution of hair color is not the same for each body type.

There is insufficient evidence to conclude that hair color and body type are dependent.

Answer 1

Ans.

We will use a Chisq test of independence to check wheter there is any association beteween hair color and body type.

Our Hypothesis will be :

H0: color and body are independent

H1: color and body type are dependent

In order to calculate the test statistic, we will make a table for expected values of the given observations.

Expected value : total of row * total of column/ Grand total

Therefore our calculated Chisq is 11.395 .

Now the P-value is given by the P( Chisq > 11.395 ) , using percentage point table for chisq , we get the value as 0.08.

Based on our P value we will reject the null hypothesis since our P-value is less than 0.10 . Thus there is sufficient evidence to conclude that body type and hair color are dependent on each other at 10 % lvl of significance.