Question

The average daily volume of a computer stock in 2011 was μ=35.1 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 28.8 million shares, with a standard deviation of s=11.1 million shares. Test the hypotheses by constructing a 95%

confidence interval. Complete parts (a) through (c) below.

Construct a

9595%

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 rejectDo not reject

the null hypothesis because

muμequals=35.135.1

million shares

does not falldoes not fall

in the confidence interval.

B.

Do not rejectDo not reject

the null hypothesis because

muμequals=35.135.1

million shares

fallsfalls

in the confidence interval.

C. Reject the null hypothesis because muμequals=35.1 million shares does not fall in the confidence interval.

D.Reject the null hypothesis because μ=35.1 million shares falls in the confidence interval.

Answer #1

Solution :

Given that,

Point estimate = sample mean = = 28.8

sample standard deviation = s = 11.1

sample size = n = 30

Degrees of freedom = df = n - 1 = 30-1 = 29

At 95% confidence level

= 1-0.95% =1-0.95 =0.05

/2
=0.05/ 2= 0.025

t/2,df
= t_{0.025,29 = 2.05}

t_{
/2,df} = 2.05

Margin of error = E = t_{/2,df}
* (s /n)

= 2.05 * (11.1/ 30)

Margin of error = E = 4.145

The 95% confidence interval estimate of the population mean is,

- E < < + E

28.8 - 4.145 < < 28.8+ 4.145

24.655 < < 32.945

(24.655,32.945)

Lower bound = 24.655

Upper bound = 32.945

= 35.1

This is the two tailed test .

The null and alternative hypothesis is

H_{0} :
= 35.1

H_{a} :
35.1

Test statistic = t

= ( - ) / s / n

= (28.8-35.1) / 11.1 / 30

= -3.109

P (Z < -3.109 ) = 0.0042

P-value = 0.0042

= 0.05

p=0.0042<0.05

C.Reject the null hypothesis because muμequals=35.1 million shares does not fall in the confidence interval.

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