Question

You measure 27 backpacks' weights, and find they have a mean weight of 38 ounces. Assume the population standard deviation is 4.4 ounces. Based on this, what is the maximal margin of error associated with a 95% confidence interval for the true population mean backpack weight.

Answer 1

Solution :

Given that,

= 38

= 4.4

n = 27

At 95% confidence level the z is ,

  = 1 - 95% = 1 - 0.95 = 0.05

/ 2 = 0.05 / 2 = 0.025

Z_/2 = Z_0.025 = 1.960

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

= 1.960 * (4.4 / 27 )

= 1.66

Margin of error = 1.66

At 95% confidence interval estimate of the population mean is,

- E < < + E

38 - 1.66 < < 38 + 1.66

36.34 < < 39.66

(36.34, 39.66)