Question

For a data set obtained from a sample of size n = 121 with x- = 44.25, it is known that σ = 5.4.

(a) What is the point estimate of µ?

(b) Find z score corresponding to a 95% confidence level, z_α/2. Recall that (1 − α)100% = 95%.

(c) Construct a 95% confidence interval for µ.

(d) What is the margin of error in part (c)?

Answer 1

Solution :

Given that,

Point estimate = sample mean = = 44.25

Population standard deviation = = 5.4

Sample size = n = 121

a) Point estimate = 44.25

b) At 95% confidence level the z is ,

= 1 - 95% = 1 - 0.95 = 0.05

/ 2 = 0.05 / 2 = 0.025

Z_/2 = Z_0.025 = 1.96

c)Margin of error = E = Z_/2* ( /n)

= 1.96 * (5.4 / 121)

= 0.96

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

- E < < + E

44.25 - 0.96< <44.25 + 0.96

43.29 < < 45.21

(43.29 ,45.21 )