Question

1. You measure 43 dogs' weights, and find they have a mean weight of 74 ounces. Assume the population standard deviation is 4.4 ounces. Based on this, construct a 95% confidence interval for the true population mean dog weight.

Give your answers as decimals, to two places

___________ ±___________

2. You measure 48 textbooks' weights, and find they have a mean weight of 77 ounces. Assume the population standard deviation is 12.3 ounces. Based on this, construct a 99.5% confidence interval for the true population mean textbook weight.

Keep 4 decimal places of accuracy in any calculations you do. Report your answers to three decimal places.

Confidence Interval

= (____________,____________)

Hint: Did you see that you are given the population standard deviation? This means the z-distribution is appropriate here instead of the t-distribution.

Answer 1

1)

sample mean, xbar = 74
sample standard deviation, σ = 4.4
sample size, n = 43

Given CI level is 95%, hence α = 1 - 0.95 = 0.05
α/2 = 0.05/2 = 0.025, Zc = Z(α/2) = 1.96

ME = zc * σ/sqrt(n)
ME = 1.96 * 4.4/sqrt(43)
ME = 1.32

CI = (xbar - Zc * s/sqrt(n) , xbar + Zc * s/sqrt(n))
CI = (74 - 1.96 * 4.4/sqrt(43) , 74 + 1.96 * 4.4/sqrt(43))
CI = (72.68 , 75.32)

74 +/- 1.32

2)

sample mean, xbar = 77
sample standard deviation, σ = 12.3
sample size, n = 48

Given CI level is 99.5%, hence α = 1 - 0.995 = 0.005
α/2 = 0.005/2 = 0.0025, Zc = Z(α/2) = 2.807

ME = zc * σ/sqrt(n)
ME = 2.807 * 12.3/sqrt(48)
ME = 4.98

CI = (xbar - Zc * s/sqrt(n) , xbar + Zc * s/sqrt(n))
CI = (77 - 2.807 * 12.3/sqrt(48) , 77 + 2.807 * 12.3/sqrt(48))
CI = (72.017 , 81.983)