Question

You measure 47 turtles' weights and find they have a mean weight of 51 ounces. Assume the population standard deviation is 14.5 ounces. Based on this, construct a 99% confidence interval for the true population mean turtle weight.

Give your answers as decimals, to two places

Answer 1

Solution :

Given that,

Point estimate = sample mean = = 51

Population standard deviation = = 14.5

Sample size = n = 47

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

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

= 2.576 * (14.5 / 47 )

= 5.45

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

- E < < + E

51 - 5.45 < < 51 + 5.45

45.55 < < 56.45

(45.55 , 56.45)