Question

A marketing firm surveys 11 people to see how much they like a certain perspective advertisement on a 0 to 10 scale. The following were the responses of the 11 people: { 4, 3, 2, 7, 5, 6, 1, 4, 3, 9, 0}. Find the approximate 95% confidence interval for the population mean. What is the lower bound? SHOW ALL STEPS

Answer 1

Solution:
Given in the question
Responses of the 11 people are as follows:
4,3,2,7,5,6,1,4.3,9,0
First, we will calculate Sample mean and observations as follows:
Sample mean = (4+3+2+7+5+6+1+4+3+9+0)/11 = 44/11 = 4
n = 11
Sample standard deviation(S) = sqrt(summation(Xi-mean)^2/(N-1))

X	Xi-mean	(Xi-mean)^2
4.00	0.00	0
3.00	-1.00	1
2.00	-2.00	4
7.00	3.00	9
5.00	1.00	1
6.00	2.00	4
1.00	-3.00	9
4.00	0.00	0
3.00	-1.00	1
9.00	5.00	25
0.00	-4.00	16

Standard deviation = sqrt(0+1+4+9+1+4+9+0+1+25+11)/10) = sqrt(70/10) = sqrt(7) = 2.65
So 95% confidence interval for a population mean can be calculated as
Mean +/- talpha/2*S/sqrt(n)
alpha = 0.05, alpha/2 = 0.025 and df= 11-1 = 10 so talpha/2 from t table is 2.2281

Mean +/- talpha/2*S/sqrt(n)
4 +/- 2.2281*2.65/sqrt(11)
4+/- 1.78
So 95% confidence interval is 2.22 to 5.78
And lower bound for 95% confidence interval is 2.22