Question

A simple random sample of size 11 is drawn from a normal
population whose standard deviation is σ=1.8. The sample mean is
¯x=26.8.

a.) Construct a 85% confidence level for μ. (Round answers to two
decimal place.)

margin of error:

lower limit:

upper limit:

b.) If the population were not normally distributed, what conditions would need to be met? (Select all that apply.)

- the population needs to be uniformly distributed
- σ is unknown
- simple random sample
- large enough sample size n
- σ is known
- systematic sampling
- the population needs to be normally distributed

Answer #1

a)

sample mean, xbar = 26.8

sample standard deviation, σ = 1.8

sample size, n = 11

Given CI level is 85%, hence α = 1 - 0.85 = 0.15

α/2 = 0.15/2 = 0.075, Zc = Z(α/2) = 1.44

ME = zc * σ/sqrt(n)

ME = 1.44 * 1.8/sqrt(11)

ME = 0.78

CI = (xbar - Zc * s/sqrt(n) , xbar + Zc * s/sqrt(n))

CI = (26.8 - 1.44 * 1.8/sqrt(11) , 26.8 + 1.44 *
1.8/sqrt(11))

CI = (26.02 , 27.58)

margin of error: 0.78

lower limit: 26.02

upper limit:27.58

b)

simple random sample

large enough sample size n

σ is known

the population needs to be normally distributed

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