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 30 trading days in​ 2014, he finds the sample mean to be 26.8 million​ shares, with a standard deviation of sequals15.1 million shares. Test the hypotheses by constructing a 95​% confidence interval. Complete parts​ (a) through​ (c) below. ​(a) State the hypotheses for the test. Upper H 0​: mu equals 35.1 million shares Upper H 1​: mu not equals 35.1 million shares ​(b) Construct a 95​% confidence interval about the sample mean of stocks traded in 2014. The lower bound is nothing million shares. The upper bound is nothing million shares. ​(Round to three decimal places as​ needed.) ​(c) Will the researcher reject the null​ hypothesis? A. Do not reject the null hypothesis because muequals35.1 million shares falls in the confidence interval. B. Do not reject the null hypothesis because muequals35.1 million shares does not fall in the confidence interval. C. Reject the null hypothesis because muequals35.1 million shares falls in the confidence interval. D. Reject the null hypothesis because muequals35.1 million shares does not fall in the confidence interval.

Answer 1

Solution:

​(a) State the hypotheses for the test.

H₀ :   = 35.1 million shares vs H₁​: 35.1 million shares

(b) Construct a 95​% confidence interval

Given that,

n = 30

= 26.8

s = 15.1

Note that, Population standard deviation() is unknown. So we use t distribution.

Our aim is to construct 95% confidence interval.

c = 0.95

= 1- c = 1- 0.95 = 0.05

  /2 = 0.05 2 = 0.025

Also, d.f = n - 1 = 30 - 1 = 29

    =    =  _0.025,29 = 2.045

( use t table or t calculator to find this value..)

The margin of error is given by

E =  /2,d.f. * ( / n )

=  2.045 * (15.1 / 30)

= 5.638

Now , confidence interval for mean() is given by:

( - E ) <   <  ( + E)

(26.8 - 5.638)   <   <  (26.8  + 5.638)

21.162 <   <  32.438

The lower bound is 21.162 million shares.

The upper bound is 32.438 million shares.

c)

Reject the null hypothesis because mu equals 35.1 million shares does not fall in the confidence interval.