Question

The average daily volume of a computer stock in 2011 was

muμequals=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 32.7 million​ shares, with a standard deviation of s equals=11.3

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.

Upper bound-

Lower bound-

​(c) Will the researcher reject the null​ hypothesis?

Answer 1

a)

null hypothesis: HO: μ		=	35.1
Alternate Hypothesis: Ha: μ		≠	35.1

b)

sample mean 'x̄=		32.700
sample size    n=		30
std deviation s=		11.300
std error ='sx=s/√n=11.3/√30=		2.0631

for 95% CI; and 29 df, value of t=		2.0452		from excel: t.inv(0.975,29)
margin of error E=t*std error    =		4.2195
lower bound=sample mean-E =		28.481
Upper bound=sample mean+E =		36.919

c)

since confidence interval contains 35.1 as a plausible value for population,we can not reject the null hypothesis