Question

For a data set obtained from a sample, n= 75 and x bar= 46.55. It is know that ?= 4.3.

a) What is the point estimate of ??

b) Make a 90% confidence interval for ?. Round answers to two decimal places.

(_________,_________)

c) What is the margin of error of estimate for part b? Round answers to three decimal places.

E=__________

Please show work for a,b,c.

Answer 1

Solution :

Given that,

a)

Point estimate = sample mean = = 46.55

Population standard deviation = = 4.3

Sample size = n = 75

At 90% confidence level the z is ,

   = 1 - 90% = 1 - 0.90 = 0.10

/ 2 = 0.10 / 2 = 0.05

Z_/2 = Z_0.05 = 1.645

c) part b)

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

= 1.645 * (4.3 / 75)

= 0.817

b)

At 90% confidence interval estimate of the population mean is,

- E < < + E

46.55 - 0.817 < < 46.55 + 0.817

45.73 < < 47.37

(45.73 , 47.37)