Question

The average daily volume of a computer stock in 2011 was 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 trading days in​ 2014, he finds the sample mean to be million​ shares, with a standard deviation of s million shares. Test the hypotheses by constructing a ​% confidence interval. Complete parts​ (a) through​ (c) below. ​(a) State the hypotheses for the test. ​: mu equals million shares ​: mu not equals million shares ​(b) Construct a ​% 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?

Answer 1

Complete question :

The average daily volume of a computer stock in 2011 was p = 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 40 trading days in 2014, he finds the sample mean to be 30.9 million shares, with a standard deviation of s = 11.8 million shares. Test the hypotheses by constructing a 95% confidence interval. Complete parts (a) through (c) below. State the hypotheses for the test. Construct a 95% confidence interval about the sample mean of stocks traded in 2014.

Answer:

H0 : μ = 35.1 ;

H1 : μ < 35.1 ;

(26.488 ; 35.312)

Explanation:

The hypothesis :

H0 : μ = 35.1

H1 : μ < 35.1

The confidence interval :

Xbar ± Margin of error

Xbar = 30.9

Margin of Error = Zcritical * s/sqrt(n)

Zcritical at 95% = 1.96

Margin of Error = 1.96 * (11.8/sqrt(40))

Margin of Error = 4.412

Lower boundary :

30.9 - 4.412 = 26.488

Upper boundary :

30.9 + 4.412 = 35.312

Confidence interval = (26.488 ; 35.312)

Since the population mean value exists within the interval, the we fail to reject the Null.