Question

A simple random sample of size 11 is drawn from a normal population whose standard deviation...

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

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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