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. a. state the hypotheses for the test. b. construct a 95% confidence interval about the sample mean of stocks traded in 2014.c. determine if the researcher

a)Null hypothesis:

Alternative hypothesis:

b) The 95% confidence interval would be given by (27.131;34.669)

c) Since the confidence interval contains the value of interest 35.1 we don't have enough evidence to reject the null hypothesis at 5% of significance.

Step-by-step explanation:

Data given and notation

represent the sample mean

s=11.8 represent the sample deviation

n=40 sample size

Confidence =0.95 or 95%

Part a

On this case the correct system of hypothesis would be:

Null hypothesis:

Alternative hypothesis:

Part b

The confidence interval for the mean is given by the following formula:  

  (1)  

In order to calculate the critical value we need to find first the degrees of freedom, given by:  

Since the Confidence is 0.95 or 95%, the value of and , and we can use excel, a calculator or a table to find the critical value. The excel command would be: "=-T.INV(0.025,39)".And we see that  

Now we have everything in order to replace into formula (1):  

So on this case the 95% confidence interval would be given by (27.131;34.669)

Part c

(c) Determine if the researcher  will reject the null hypothesis.

Since the confidence interval contains the value of interest 35.1 we don't have enough evidence to reject the null hypothesis at 5% of significance.

a. is correct

the ratio of balloons to tables is 5: 2 and the constant variation is 5.

the equation is y=5x