Question

An analyst is trying to determine whether the prices of certain stocks on the NASDAQ are independent of the industry to which they belong. She examines four industries and classifies the stock prices in these industries into one of three categories (high-priced, average-priced, low-priced).

- Provide the competing hypotheses to determine whether stock price depends on the industry.

- Use Minitab to calculate the value of the test statistic and approximate the p-value.

- At a 1% significance level, what can the analyst conclude?

Stock Price	Industry
	I	II	III	IV
High	16	8	10	14
Average	18	16	10	12
Low	7	8	4	9

Answer 1

here we use chi-square test with

null hypothesis H0: stock price and  industry are independent ( or stock price doest not depend on the industry)

alternate hypothesis Ha: stock price and  industry are not independent ( or stock price depends on the industry)

and chi-square=sum((O-E)²/E)=3.65 with (r-1)(c-1)=(3-1)(4-1)=6 df

p-value=0.7239 is more than level of significance alpha=0.01, so we fail to reject H0(or accept H0) and conclude that stock price does not depend on the industry.

	Observed(O)	Expected (E)	E	(O-E)	(O-E)2/E
	16	41*48/132	14.91	1.09	0.08
	18	41*56/132	17.39	0.61	0.02
	7	41*28/132	8.70	-1.70	0.33
	8	32*48/132	11.64	-3.64	1.14
	16	32*56/132	13.58	2.42	0.43
	8	32*28/132	6.79	1.21	0.22
	10	24*48/132	8.73	1.27	0.19
	10	24*56/132	10.18	-0.18	0.00
	4	24*28/132	5.09	-1.09	0.23
	14	35*48/132	12.73	1.27	0.13
	12	35*56/132	14.85	-2.85	0.55
	9	35*28/132	7.42	1.58	0.33
sum	132	0	132	1.78E-15	3.65E+00