Question

You measure 35 textbooks' weights, and find they have a mean weight of 57 ounces. Assume the population standard deviation is 10.2 ounces. Based on this, construct a 99% confidence interval for the true population mean textbook weight .

Give your answers as decimals, to two places

Answer 1

Solution :

Given that,

Point estimate = sample mean = = 57

Population standard deviation =    = 10.2
Sample size = n =35

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 * ( 10.2/ 35)

= 4.44

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

- E < < + E

57-4.44 < <57+4.44

52.56< < 61.44

(52.56 , 61.44)