Question

The following data were randomly drawn from an approximately normal population.

37, 40, 43, 45, 49

Based on these data, find a 95% confidence interval for the population standard deviation. Then complete the table below.

Carry your intermediate computations to at least three decimal places. Round your answers to at least two decimal places.

What is the lower limit of the 95% confidence interval? What is the upper limit of the 95% confidence interval?

Answer 1

Solution:

x	x2
37	1369
40	1600
43	1849
45	2025
49	2401
∑x=214	∑x2=9244

Mean ˉx=∑xn

=37+40+43+45+495

=2145

= 42.8

Population Standard deviation σ=√∑x2-(∑x)2nn

=√9244-(214)25/5

=√9244-9159.2/5

=√84.8/5

=√16.96

=4.1183

At 95% confidence level the z is ,

  = 1 - 95% = 1 - 0.95 = 0.05

/ 2 = 0.05 / 2 = 0.025

Z/2 = Z0.025 = 1.960

Margin of error = E = Z/2* (/n)

= 1.960 * (4.118 / 5 )

= 8.48

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

- E < < + E

42.8 - 8.48< < 42.8 + 8.48

59.8 < < 65.2

The lower limit = 34.32

The upper limit = 51.28