Question

You measure 37 textbooks' weights, and find they have a mean weight of 34 ounces. Assume the population standard deviation is 14.9 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 = = 34

Population standard deviation =    = 14.9

Sample size = n =37

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 * ( 14.9/ 37)

E= 6.31

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

- E < < + E

34-6.31 < <34+ 6.31

24.69< < 40.31

(24.69, 40.31 )