Question

Assuming a sample is taken and it's mean is calculated as 240. For 90% of the confidence interval for μ, the upper limit comes to 280. What is the lower limit of the confidence interval
a) 220
b) 240
c) 200
d) cannot determined from the information given

Answer 1

Answer:

option b is the right answer 240

Answer 2

Answer:

b) 240

Step-by-step explanation:

A confidence interval for a population mean with a known population standard deviation is based on the conclusion of the Central Limit Theorem that the sampling distribution of the sample means follow an approximately normal distribution.

Consider the standardizing formula for the sampling distribution developed in the discussion of the Central Limit Theorem:

${Z}_{1}=\frac{\stackrel{-}{X}-{\mu }_{\stackrel{-}{X}}}{{\sigma }_{\stackrel{-}{X}}}=\frac{\stackrel{-}{X}-\mu }{\sigma }{\sqrt{n}}}$

Notice that µ is substituted for ${µ}_{\stackrel{-}{x}}$because we know that the expected value of${µ}_{\stackrel{-}{x}}$ is µ from the Central Limit theorem and${\sigma }_{\stackrel{-}{x}}$is replaced with $\sigma }{\sqrt{n}}$, also from the Central Limit Theorem.

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