Question

The average daily volume of a computer stock in 2011 was muequals35.1 million​ shares, according to a reliable source. A stock analyst believes that the stock volume in 2014 is different from the 2011 level. Based on a random sample of 40 trading days in​ 2014, he finds the sample mean to be 26.7 million​ shares, with a standard deviation of sequals15.4 million shares. Test the hypotheses by constructing a 95​% confidence interval. Complete parts​ (a) through​ (c) below. ​(a) State the hypotheses for the test. ​(b) Construct a 95​% confidence interval about the sample mean of stocks traded in 2014. c) reject or fail?

Answer 1

(a)

H0: Null Hypothesis: = 35.1

HA: Alternative Hypothesis : 35.1

(b)

SE = s/

= 15.4/ = 2.4350

= 0.05

ndf = n - 1= 40 - 1= 39

From Table, critical values of t = 2.0227

Confidence Interval:

26.7 (2.0227 X 2.4350)

= 26.7 4.9252

= ( 21.7748 ,31.6252)

Confidence Interval:

21.7748 < < 31.6252

(c)

Test statistic is given by:

t = (26.7 - 35.1)/2.4350 = - 3.45

Since calculated value of t = - 3.45 is less than critical value of t = - 2.0227, the difference issignificant. Reject null hypothesis.

So,

Correct option:

reject