Question

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:

Download the data

Daily returns (%)
1.039	0.626	0.267	0.389	-0.066	1.549	0.698	1.6	0.761	-1.392	0.718	0.885
-0.154	0.894	-0.24	1.366	0.625	-0.279	0.027	0.429	0.951	1.449	1.995	1.131
2.049	2.932	1.935	-0.911	2.24	1.46	0.644	1.45	1.799	0.677	1.568	1.24
0.878	1.159	0.879	1.053	1.859	0.08	0.489	-0.756	0.325	0.125	0.335	1.483
1.517	2.525	0.739	1.147	0.354	3.04	0.512	0.485	-3.311	1.978	1.326	0.295
-0.272	1.235	0.176	1.127	1.324	2.366	0.262	1.842	-0.52	-0.335	2.027	2.639
0.713	2.337	0.141	1.385	2.316	-0.142	1.744	-0.503	-0.567	-0.446	1.176	0.122
-0.331	0.098	0.22	1.072	-0.079	0.49	0.405	0.531	2.242	-0.429	0.3	-0.81
0.551	2.201	-0.315	2.392	0.038	-0.616	1.825	3.129	-0.319	0.404	0.696	0.74
0.795	-1.872	1.128	1.58	1.531	0.182	-1.597	-1.231	0.758	1.078	-2.278	0.708

Historically, the standard deviation in daily return for this stock is 1.1%.

Complete the report to your boss. Give your numeric answers to 3 decimal places.

Sent:	July 24, 2019 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 1.1%, the 95% confidence interval for the mean daily return is:

a) ≤ μ ≤

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

Answer 1

b) This means that

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