Question

Assuming the population is normally distributed, construct a 95% confidence interval for the population mean, based on the following sample of size n = 7:

1 2 3 4 5 6 7

The mean is 4 and Standard Deviation 2.16

1. What is the lower boundary of the interval to two decimal places?

2. What is upper boundary of the interval to two decimal.

Answer 1

Solution :

Given that,

Point estimate = sample mean = = 4

sample standard deviation = s = 2.16

sample size = n = 7

Degrees of freedom = df = n - 1 = 6

At 95% confidence level the t is ,

= 1 - 95% = 1 - 0.95 = 0.05

/ 2 = 0.05 / 2 = 0.025

t _/2,df = t_0.025,6 = 2.447

Margin of error = E = t_/2,df * (s /n)

= 2.447* ( 2.16/ 7)

= 2.00

The 95% confidence interval estimate of the population mean is,

- E < < + E

4 - 2.00 < < 4 + 2.00

2.00 < < 6.00

(2.00,6.00)

1)

The lower boundary of the interval is 2.00

2)

The upper boundary of the interval is 6.00