Question

Researchers were interested in the relationship between the type of prison the inmate is attending (High, Medium, Minimum) and the prison history of their parents (Both, None, One).  Below is the two-way table of the observed data.

	High	Medium	Minimum	Total
Both	15	22	12	49
None	61	125	47	233
One	50	108	60	218
Total	126	255	119	500

What proportion of inmates with both parents in prison are in high security prisons?

If there was no relationship between the type of prison and the prison history of their parents, what proportion of inmates with both parents in prison would be in high security prisons?

The researchers are interested in testing the relationship between prison history of the parents and the type of prison an inmate is attending. What are the appropriate null and alternative hypotheses to test this relationship?

What are the degrees of freedom for the Chi Square test?

What are the missing expected counts under the null hypothesis?

	High	Medium	Minimum	Total
Both	12.3	25.0	11.7	49
None	58.7	118.8		233
One		111.2	51.9	218
Total	126	255	119	500

If the P-value is greater than 0.25, is there evidence of a relationship between the prison history of the parents and the type of prison an inmate is attending?

Answer 1

usig excel>Addin>phstat>multiple sample test

we have

Chi-Square Test
Observed Frequencies
	Column variable			Calculations
Row variable	High	Medium	Minimum	Total		fo-fe
Both	15	22	12	49		2.652	-2.99	0.338
None	61	125	47	233		2.284	6.17	-8.454
One	50	108	60	218		-4.936	-3.18	8.116
Total	126	255	119	500
Expected Frequencies
	Column variable
Row variable	High	Medium	Minimum	Total		(fo-fe)^2/fe
Both	12.348	24.99	11.662	49		0.569574	0.357747	0.009796
None	58.716	118.83	55.454	233		0.088846	0.320364	1.288818
One	54.936	111.18	51.884	218		0.4435	0.090955	1.269552
Total	126	255	119	500
Data
Level of Significance	0.05
Number of Rows	3
Number of Columns	3
Degrees of Freedom	4
Results
Critical Value	9.487729
Chi-Square Test Statistic	4.439153
p-Value	0.349823
Do not reject the null hypothesis

the appropriate null and alternative hypotheses to test this relationship are

Ho:there is no relationship between the prison history of the parents and the type of prison an inmate is attending

HA::there is a relationship between the prison history of the parents and the type of prison an inmate is attending

the degrees of freedom for the Chi Square test is 4

the missing expected counts under the null hypothesis are

	High	Medium	Minimum	Total
Both	12.3	25.0	11.7	49
None	58.7	118.8	55.5	233
One	54.9	111.2	51.9	218
Total	126	255	119	500

If the P-value is greater than 0.25, then there is not sufficient evidence of a relationship between the prison history of the parents and the type of prison an inmate is attending. because ho is accepted