Question

You measure 50 textbooks' weights, and find they have a mean weight of 32 ounces. Assume the population standard deviation is 2.9 ounces. Based on this, construct a 99% confidence interval for the true population mean textbook weight.

Give your answers as decimals, to two places

I am 99% confident that the mean weight of textbooks is between and ounces.

Answer 1

Solution :

Given that,

Point estimate = sample mean = = 32

Population standard deviation =    = 2.9
Sample size = n =50

At 99% confidence level the z is ,

  = 1 - 99% = 1 - 0.99 = 0.01

/ 2 = 0.01 / 2 = 0.005

Z/2 = Z0.005 = 2.576   ( Using z table )

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

= 2.576* ( 2.9/ 50)

= 1.06

At 99% confidence interval estimate of the population mean is,

- E < < + E

32-1.06 < < 32+1.06

30.94< <33.06

(,30.94,33.06 )