Question

2

Apr. 30, 2009	35	38	26	29	30	34
Jan. 1, 2009	28	30	27	24	30	20

A statistical analyst for the Wall Street Journal randomly selected six companies and recorded both the price per share of stock on January 1, 2009 and on April 30, 2009. The results are presented below. Suppose the analyst wished to see if the average price per share of stock on April 30, 2009 is greater than the average price per share of stock on January 1, 2009 at α=.05.

For the hypothesis stated above, what is the decision (in terms of "April 30, 2009" minus "January 1, 2009")?

	a.	None of the answers is correct
	b.	Fail to reject H0 because the test statistic is to the right of the positive critical value
	c.	Reject H0 because the test statistic is to the right of the positive critical value
	d.	Fail to reject H0 because P-value > α
	e.	Reject H0 because P-value > α

Answer 1

Below are the null and alternative Hypothesis,
Null Hypothesis: μ(d) = 0
Alternative Hypothesis: μ(d) > 0

Test statistic,
t = (dbar - 0)/(s(d)/sqrt(n))
t = (5.5 - 0)/(5.5408/sqrt(6))
t = 2.431

P-value Approach
P-value = 0.0297
As P-value < 0.05, reject the null hypothesis.

Rejection Region
This is right tailed test, for α = 0.05 and df = 5
Critical value of t is 2.02.
Hence reject H0 if t > 2.02

option C
  
Reject H0 because the test statistic is to the right of the positive critical value