Question

You measure 38 watermelons' weights, and find they have a mean weight of 47 ounces. Assume the population standard deviation is 8.7 ounces. Based on this, construct a 99% confidence interval for the true population mean watermelon weight. Give your answers as decimals, to two places ± ounces

Answer 1

Solution

Given that,

= 47

= 8.7

n = 38

At 99% confidence level the z is ,

= 1 - 99% = 1 - 0.99 = 0.01

/ 2 = 0.01 / 2 = 0.005

Z_/2 = Z_0.005 = 2.576

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

= 2.576 * (8.7 / 38 )

= 3.64

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

- E < < + E

47 - 3.64 < < 47 + 3.64

43.36 < < 50.64

(43.36 ,50.64)