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).

    Industry
Stock Price   I   II   III   IV
High   22   13   17   22
Average   16   14   16   26
Low   16   8   4   13

Click here for the Excel Data File

a. Choose the competing hypotheses to determine whether stock price depends on the industry.

H0: Stock price is dependent on the industry.; HA: Stock price is independent on the industry.
H0: Stock price is independent of the industry.; HA: Stock price is dependent on the industry.

b-1. Calculate the value of the test statistic. (Round intermediate calculations to at least 4 decimal places and final answer to 3 decimal places.)

b-2. Find the p-value.

p-value < 0.01
0.01 p-value < 0.025
0.025 p-value < 0.05
0.05 p-value < 0.10
p-value 0.10

c. At a 10% significance level, what can the analyst conclude?

Do not reject H0; there is not enough evidence to support the claim that the stock price is dependent on the industry.
Reject H0; there is enough evidence to support the claim that the stock price is dependent on the industry.
Reject H0; there is not enough evidence to support the claim that the stock price is dependent on the industry.
Do not reject H0; there is enough evidence to support the claim that the stock price is dependent on the industry.

Answer 1

The statistical software output for this problem is:

Chi-Square test:

Statistic	DF	Value	P-value
Chi-square	6	5.8206547	0.4436

Hence,

a) Hypotheses: H0: Stock price is independent of the industry.; HA: Stock price is dependent on the industry.

Option B is correct.

b - 1) Test statistic = 5.821

b - 2) p-value > 0.10

c) Do not reject H0; there is not enough evidence to support the claim that the stock price is dependent on the industry.

Option A is correct.