Question

You are investigating the relationship between the ages of adults and what aspect of career development they consider to be the most important. You randomly collect the data shown in the contingency table. At alpha equals 0.01​, is there enough evidence to conclude that age is related to which aspect of career development is considered to be most​ important? Perform the​ chi-square independence test by completing parts​ (a) through​ (e) below. Career development aspect Age Learning new skills Pay increases Career path ​ 18-26 years 33 21 21 ​ 27-41 years 26 30 35 ​ 42-62 years 21 13 9 ​(a) Identify the claim and state Upper H 0 and Upper H Subscript a. Upper H 0​: The aspect of career development that is considered to be most important is independent of age. Upper H Subscript a​: The aspect of career development that is considered to be most important is dependent on age. Which hypothesis is the​ claim? Alternative hypothesis Your answer is correct. Null hypothesis ​(b) Determine the degrees of​ freedom, find the critical​ value, and identify the rejection region. Calculate the degrees of freedom. d.f.equals 4 Find the critical value. chi Subscript 0 Superscript 2equals nothing ​(Round to three decimal places as​ needed.) Enter your answer in the answer box and then click Check Answer.

Answer 1

b)

degree of freedom(df) =(rows-1)*(columns-1)=

4

cirtical value =13.277

rejection region:X² >13.277

Applying chi square test:

Expected	Ei=row total*column total/grand total	learning new skills	pay increase	Career Path	Total
	18-26	28.71	22.97	23.33	75
	27-41	34.83	27.87	28.30	91
	42-62	16.46	13.17	13.37	43
	total	80	64	65	209
chi square    χ2	=(Oi-Ei)2/Ei	learning new skills	pay increase	Career Path	Total
	18-26	0.6416	0.1684	0.2318	1.042
	27-41	2.2397	0.1634	1.5855	3.989
	42-62	1.2526	0.0021	1.4301	2.685
	total	4.134	0.334	3.247	7.7153

test statistic X² =7.715

fail to reject Ho.