Question

Date	Apple Close Price	Monthly Return
11/1/13	76.825317	7.01%
12/2/13	77.509201	0.89%
1/2/14	69.161713	-10.77%
2/3/14	73.139267	5.75%
3/3/14	74.59861	2.00%
4/1/14	82.013435	9.94%
5/1/14	88.468651	7.87%
6/2/14	90.915863	2.77%
7/1/14	93.527992	2.87%
8/1/14	100.777245	7.75%
9/2/14	99.056656	-1.71%
10/1/14	106.184807	7.20%
11/3/14	117.438133	10.60%
12/1/14	108.995377	-7.19%
1/2/15	115.690338	6.14%
2/2/15	127.34922	10.08%
3/2/15	123.354057	-3.14%
4/1/15	124.067833	0.58%
5/1/15	129.692947	4.53%
6/1/15	124.864807	-3.72%
7/1/15	120.753418	-3.29%
8/3/15	112.760002	-6.62%
9/1/15	110.300003	-2.18%
10/1/15	111.730003	1.30%

Calculate the following sample statistics for the "Monthly Return" Variable:

Sample size n ==>

Sample Mean X-Bar ==>

Sample Variance S2 ==>

Q3. Based on these sample statistics, calculate the LCL and UCL for a 95% confidence intercal of the mean monthly return.

a. LCL ==>

b. UCL ==>

Answer 1

Here sample size is n=24

Sample mean is

Create the following table.

data	data-mean	(data - mean)2
7.01	4.9825	24.82530625
0.89	-1.1375	1.29390625
-10.77	-12.7975	163.77600625
5.75	3.7225	13.85700625
2	-0.0275	0.00075625
9.94	7.9125	62.60765625
7.87	5.8425	34.13480625
2.77	0.7425	0.55130625
2.87	0.8425	0.70980625
7.75	5.7225	32.74700625
-1.71	-3.7375	13.96890625
7.2	5.1725	26.75475625
10.6	8.5725	73.48775625
-7.19	-9.2175	84.96230625
6.14	4.1125	16.91265625
10.08	8.0525	64.84275625
-3.14	-5.1675	26.70305625
0.58	-1.4475	2.09525625
4.53	2.5025	6.26250625
-3.72	-5.7475	33.03375625
-3.29	-5.3175	28.27580625
-6.62	-8.6475	74.77925625
-2.18	-4.2075	17.70305625
1.3	-0.7275	0.52925625

Find the sum of numbers in the last column to get.

Now to find CI, let us assume that distribution is normal, as n<30 we will use t distribution

So t table value for 95% CI is 2.069

Hence Margin of Error is

So CI is

Hence LCL =-0.4708

& UCL=4.5258