Q1. (20 pts)The volume of a stock is the number of shares traded in the stock in

Question

Q1. (20 pts)The volume of a stock is the number of shares traded in the stock in a day. The mean volume of Apple stock in 2007 was 35.14 million shares with a standard deviation of 15.07 million shares. A stock analyst believes that the volume of Apple stock has increased since then. He randomly selects 40 trading days in 2008 and determines the sample mean volume to be 41.06 million shares. Test the analyst's claim at the -0.10 level of significance a) Using critical Iclassical value approach b) Using p-value approach c) Test the hypotheses presented in Question3 at the F0.05 level of significance by constructing a 95% confidence interval about the population mean can content.

Explanation / Answer

here null hypothesis:Ho: <=35.14

alternate hypothesis:Ha: >35.14

a) for 0.1 level and right tail test critical value z=1.28

Decision rule: reject Ho if test statistic z>1.28

here std error of mean =std deviation/(n)1/2 =15.07/(40)1/2 =2.383

therefore test statistic z=(X-mean)/std error =(41.06-35.14)/2.383=2.484

as test statistic is higher then critical value ; we reject null hypothesis and conclude that volume of apple stock has increased since then

b) for above test statistic ; p value =0.0065 ' as p value is lower then 0.05 level of significance  we reject null hypothesis and conclude that volume of apple stock has increased since then

c)

here for 95% Ci ; critical value of z =1.96

therfore 95% confidence interval for mean =sample mean -/+z*Std error =41.06 -/+ 1.96*2.383 =36.39 ; 45.73

as above confidence interval does not contain value 0 in its interval value ;  we reject null hypothesis and conclude that volume of apple stock has increased since then

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