Question

You measure 22 dogs' weights, and find they have a mean weight of 35 ounces. Assume the population standard deviation is 13.4 ounces. Based on this, construct a 95% confidence interval for the true population mean dog weight. Give your answers as decimals, to two places

You measure 43 textbooks' weights, and find they have a mean weight of 49 ounces. Assume the population standard deviation is 13 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 :

a) 95% confidence interval for the true population mean dog weight

Given that,

= 35

= 13.4

n = 22

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 = 1.96

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

= 1.96 * (13.4 /22)

= 5.60

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

- E < < + E

35 - 5.60 < < 35 + 5.60

29.40 < < 40.60

(29.40, 40.60)

b) 99% confidence interval for the true population mean textbook weight.

Given that,

= 49

= 13

n = 43

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 * (13 / 43)

= 5.11

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

- E < < + E

49 - 5.11 < < 49 + 5.11

43.89 < < 54.11

(43.89, 54.11)

(, )