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 31.5 million​ shares, with a standard deviation of s=12.3 million shares. Test the hypotheses by constructing a 95​% confidence interval.

State the hypotheses for the test.

H0​: _______ _______35.1 million shares

H1​: _______ _______35.1 million shares

Answer 1

Answer)

Null hypothesis Ho : u = 35.1

Alternate hypothesis Ha : u is not equal to 35.1

Given information

Sample mean = 31.5

S.d = 12.3

N = 30

As the population s.d is unknown here and we are using sample standard deviation as the best esimate, so we will use t distribution table to construct the interval

Degrees of freedom is equal to n-1, 29

For df 29 and 95% confidence level critical value t from t table is = 2.045

Margin of error (MOE) = t*(s.d/√n)

MOE = 4.59237978340

Confidence interval is given by

(Mean - MOE, Mean + MOE)

(26.9076202165, 36.0923797834)

As null hypothesized value 35.1 is inside the interval, we fail to reject Ho (null hypothesis)

And we do not have enough evidence to support the claim.