As a stock analyst, your boss, Jerry, has asked you to compile some information on stock of Southern Infrastructure Corporation including a 95% confidence interval for the mean daily return that he needs to include in a report to senior management. He says that he is also not sure exactly what a 95% confidence interval means and would like you to add an explanation.
You have been following the share price of Southern Infrastructure Corporation and have recorded the daily return (as a percentage) for the last 120 days. The data is presented here:
mean=44.2020
Historically, the standard deviation in daily return for this stock is 1.0%.
Complete the report to your boss. Give your numeric answers to 3 decimal places.
Sent: February 26, 2015 11:10 AM
To: Jerry Kendall
Subject: Southern Infrastructure Corp. stock info
Dear Jerry,
Here are the results gathered from the collected data:
Assuming a population standard deviation in daily return of 1.0%, the 95% confidence interval for the mean daily return is:
a) ? ? ?
b)This means that
approximately 95% of sample means will be within the interval given above
using a process that gives correct results in 95% of cases, the population mean daily return is within the interval given above
the population mean daily return is definitely within the interval given above
on approximately 95% of days in a given period the stock makes a return within the interval given above

Given that as a stock analyst, your boss, Jerry, has asked you to compile some information on stock of Southern Infrastructure Corporation including a 95% confidence interval for the mean daily return that he needs to include in a report to senior management. He says that he is also not sure exactly what a 95% confidence interval means and would like you to add an explanation.

Population std deviation= historic std dev = 1.0% = 0.01

Mean value = 44.2020 (sample mean is taken as estimate for population mean)

Std error of sample = population std dev/square root of n

Here n =120

So std error = [tex]\frac{1}{\sqrt{120} } =0.0913[/tex]

Since population std deviation is known and sample size is large we use Z critical value for 95% = 1.96

Confidence interval 95% = Mean±1.96*std error

= [tex](44.2020-1.96*0.0913, 44.2020+1.96*0.0913)\\= (44.0231, 44.3809)[/tex]

a) (44.0231, 44.3809)

b)This means that

approximately 95% of sample means will be within the interval given above

using a process that gives correct results in 95% of cases, the population mean daily return is within the interval given above

the population mean daily return is definitely within the interval given above

on approximately 95% of days in a given period the stock makes a return within the interval given abov