Question

College students may be interested in whether or not their majors have any effect on starting salaries after graduation. Suppose that 293 recent graduates were surveyed as to their majors in college and their starting salaries after graduation. Below are the data. Conduct a test of independence. (Use a significance level of 0.05.)

• What is the test statistic? (Round your answer to two decimal places.)

• Part (f)

  What is the p-value? (Round your answer to four decimal places.)
  
  
  Explain what the p-value means for this problem.If

  H₀

  is false, then there is a chance equal to the p-value that the value of the test statistic will be equal to or less than the calculated value. If

  H₀

  is false, then there is a chance equal to the p-value that the value of the test statistic will be equal to or greater than the calculated value.     If

  H₀

  is true, then there is a chance equal to the p-value that the value of the test statistic will be equal to or less than the calculated value. If

  H₀

  is true, then there is a chance equal to the p-value that the value of the test statistic will be equal to or greater than the calculated value.

Major	< $50,000	$50,000 - $68,999	$69,000 +
English	4	19	4
Engineering	9	29	59
Nursing	10	14	15
Business	11	20	29
Psychology	20	30	20

Answer 1

Applying chi square test of independence:

Expected	Ei=row total*column total/grand total	f	g	h	Total
	a	4.98	10.32	11.70	27
	b	17.88	37.08	42.04	97
	c	7.19	14.91	16.90	39
	d	11.06	22.94	26.01	60
	e	12.90	26.76	30.34	70
	total	54	112	127	293
chi square    χ2	=(Oi-Ei)2/Ei	f	g	h	Total
	a	0.191	7.299	5.070	12.5604
	b	4.408	1.760	6.838	13.0060
	c	1.100	0.055	0.215	1.3702
	d	0.000	0.376	0.344	0.7204
	e	3.906	0.393	3.525	7.8238
	total	9.6065	9.8826	15.9918	35.4808
test statistic X2 =		35.48
p value =		0.0000

If H₀ is true, then there is a chance equal to the p-value that the value of the test statistic will be equal to or greater than the calculated value.