Question

In: Statistics and Probability

The average daily volume of a computer stock in 2011 was μ equals = 35.1 million​...

The average daily volume of a computer stock in 2011 was μ equals = 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 25.5 million​ shares, with a standard deviation of s= 15.2 million shares. Test the hypotheses by constructing a 95​% confidence interval. Complete parts​ (a) through​ (c) below.

B.) Construct a 95​% confidence interval about the sample mean of stocks traded in 2014. The lower bound is ____ million shares.

The upper bound is _____ million shares.

C.)Will the researcher reject the null hypothesis?

A. Reject the null hypothesis because μ = 35.1 million shares falls in the confidence interval.

B. Do not reject the null hypothesis because u=35.1 million shares does not fall in the confidence interval.

C. Do not reject the null hypothesis because u=35.1 million shares falls in the confidence interval.

D. Reject the null hypothesis because u=35.1 million shares does not fall in the confidence interval.

Solutions

Expert Solution

b)

sample std dev ,    s =    15.2000
Sample Size ,   n =    40
Sample Mean,    x̅ =   25.5000

Level of Significance ,    α =    0.05          
degree of freedom=   DF=n-1=   39          
't value='   tα/2=   2.0227   [Excel formula =t.inv(α/2,df) ]      
                  
Standard Error , SE = s/√n =   15.200   / √   40   =   2.4033
margin of error , E=t*SE =   2.0227   *   2.403   =   4.861
                  
confidence interval is                   
Interval Lower Limit = x̅ - E =    25.50   -   4.861   =   20.6388
Interval Upper Limit = x̅ + E =    25.50   -   4.861   =   30.3612
95%   confidence interval is (   20.64   < µ <   30.36   )

c)

Ho :   µ =   35.1
Ha :   µ ╪   35.1

D. Reject the null hypothesis because u=35.1 million shares does not fall in the confidence interval.


Related Solutions

The average daily volume of a computer stock in 2011 was h=35.1 million​ shares, according to...
The average daily volume of a computer stock in 2011 was h=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 30.1 million​ shares, with a standard deviation of s=14.3 million shares. Test the hypotheses by constructing a 95​% confidence interval. Complete parts​ (a) through​ (c) below.
1. The average daily volume of a computer stock in 2011 was μ= 35.1million​ shares, according...
1. The average daily volume of a computer stock in 2011 was μ= 35.1million​ 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 28.5 million​ shares, with a standard deviation of s=12million shares. Test the hypotheses by constructing a 95​% confidence interval. Complete parts​ (a) through​ (c) below. a....
The average daily volume of a computer stock in 2011 was muequals35.1 million​ shares, according to...
The average daily volume of a computer stock in 2011 was muequals35.1 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 26.8 million​ shares, with a standard deviation of sequals15.1 million shares. Test the hypotheses by constructing a 95​% confidence interval. Complete parts​ (a) through​ (c) below. ​(a)...
The average daily volume of a computer stock in 2011 was mu equals35.1 million​ shares, according...
The average daily volume of a computer stock in 2011 was mu equals35.1 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 28.9 million​ shares, with a standard deviation of sequals 11.2 million shares. Test the hypotheses by constructing a 95 ​% confidence interval. Complete parts​ (a) through​...
The daily market transactions for treasury instruments are in the billions. The current average daily volume...
The daily market transactions for treasury instruments are in the billions. The current average daily volume of “Treasuries” is approximately $150 billion. Like you, corporations may have extra cash to invest. In this case, you, as a finance manager, are considering investing $50,000 in either a Treasury bill that you will renew every 6 months or investing in a 5-year Treasury note that you will hold until maturity. Current interest rates are expected to increase. Would you invest in the...
A wastewater treatment plant, which serves a population of 300,000 people, receives an average daily volume...
A wastewater treatment plant, which serves a population of 300,000 people, receives an average daily volume of 24 million gallons per day (MGD) at an average influent 5-day biochemical oxygen demand concentration of 200 mgBOD5/L and an average influent total suspended solids concentration of 220 mgTSS/L. The plant operates a primary sedimentation process that remove 65% of the incoming TSS and 35% of the incoming BOD5%. This process is followed by a secondary treatment process before discharge to the local...
A random sample of 100 daily stock returns was taken. The average return in the sample...
A random sample of 100 daily stock returns was taken. The average return in the sample appeared to be 4.81%. The population standard deviation is not known, but the sample standard deviation is known to be 0.9%. (show your work) a. Calculate a 95% confidence interval for the average stock return b. How big the sample size be for the margin of error of 0.1% at the confidence level 95%? c. A fund manager claims that the average stock return...
A random sample of 100 daily stock returns was taken. The average return in the sample...
A random sample of 100 daily stock returns was taken. The average return in the sample appeared to be 4.81%. The population standard deviation is not known, but the sample standard deviation is known to be 0.9%. a.  Calculate a 95% confidence interval for the average stock return b. How big the sample size be for the margin of error of 0.1% at the confidence level 95%? c. A fund manager claims that the average stock return is higher than 4.81%....
A firm’s annual credit sales are $1.34 million, with 51% of its daily average paid out...
A firm’s annual credit sales are $1.34 million, with 51% of its daily average paid out in purchases. It usually takes the company 30 days to meet its purchasing obligations. This payment pattern has not changed in recent years. However, the firm’s commitment to accounts receivable has shifted based on its current annual net income of $28k which meets the 2.3% required return, anticipated by senior management a year earlier. Normally, the firm collects its accounts in 24 days, an...
A small stock brokerage firm wants to determine the average daily sales (in dollars) of stocks...
A small stock brokerage firm wants to determine the average daily sales (in dollars) of stocks to their clients. A sample of the sales for 30 days revealed an average daily sales of $200,000. Assume that the standard deviation of the population is known to be $20,000. 8. Provide a 90% confidence interval estimate for the true average daily sales. 9. Provide a 97% confidence interval estimate for the true average daily sales.
ADVERTISEMENT
ADVERTISEMENT
ADVERTISEMENT