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)

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