Question

A fitness trainer is interested in investigating whether ethnicity and the first exercise activity that members engage in are dependent. The table below shows the results of the trainer's observation of randomly selected members.

Frequencies of Ethnicity and Exercise Activity

CardioWeight MachinesFree Weights

White849487

Hispanic868887

Black525351

Other656857

What can be concluded at the  = 0.01 significance level?

What is the correct statistical test to use?

Independence

Paired t-test

Homogeneity

Goodness-of-Fit

What are the null and alternative hypotheses?

Ethnicity and first exercise activity are dependent.

Ethnicity and first exercise activity are independent.

The distribution of first exercise activity is not the same for each ethnicity.

The distribution of first exercise activity is the same for each ethnicity.

The distribution of first exercise activity is not the same for each ethnicity.

Ethnicity and first exercise activity are independent.

Ethnicity and first exercise activity are dependent.

The distribution of first exercise activity is the same for each ethnicity.

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)   

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 ethnicity and first exercise activity are independent.

There is insufficient evidence to conclude that the distribution of first exercise activity is not the same for each ethnicity.

There is sufficient evidence to conclude that the distribution of first exercise activity is not the same for each ethnicity.

There is insufficient evidence to conclude that ethnicity and first exercise activity are dependent.

There is sufficient evidence to conclude that ethnicity and first exercise activity are dependent.

Answer 1

using excel>add in>phstat>multiple sample test

we have

Chi-Square Test
Observed Frequencies
	Column variable			Calculations
Row variable	cardio	free weight	machines weight	Total		fo-fe
White	84	94	87	265		-3.21904	1.918578	1.300459
Hispanic	86	88	87	261		0.097477	-2.69151	2.594037
Black	52	53	51	156		0.655963	-1.20642	0.550459
other	65	68	57	190		2.465596	1.979358	-4.44495
Total	287	303	282	872
Expected Frequencies
	Column variable
Row variable	cardio	free weight	machines weight	Total		(fo-fe)^2/fe
White	87.21904	92.08142	85.69954	265		0.118807	0.039975	0.019734
Hispanic	85.90252	90.69151	84.40596	261		0.000111	0.079878	0.079722
Black	51.34404	54.20642	50.44954	156		0.00838	0.02685	0.006006
other	62.5344	66.02064	61.44495	190		0.097213	0.059343	0.32155
Total	287	303	282	872
Data
Level of Significance	0.01
Number of Rows	4
Number of Columns	3
Degrees of Freedom	6
Results
Critical Value	16.81189
Chi-Square Test Statistic	0.857569
p-Value	0.990441
Do not reject the null hypothesis

What is the correct statistical test to use?

Independence

What are the null and alternative hypotheses?

Ho:Ethnicity and first exercise activity are independent.

Ha:Ethnicity and first exercise activity are dependent.

The test-statistic for this data = 0.858

The p-value for this sample =0.990

The p-value is greater than (or equal to) alpha  

Based on this, we should

fail to reject the null

Thus, the final conclusion is...

There is sufficient evidence to conclude that ethnicity and first exercise activity are independent.