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A simple random sample of size n is drawn from a population that is normally distributed....

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Statistics

A simple random sample of size n is drawn from apopulation that is normally distributed. The sample mean, x, isfound to be 50, and the sample standard deviation, s, is found tobe 8.

a) Describe the sampling distribution of the sample meanx.

b) Construct a 98% confidence interval for μ if thesample size, n, is 20.

c) Construct a 98% confidence interval for μ if thesample size, n, is 15. How does decreasing the sample size affectthe margin of error, E?

d) Construct a 95% confidence interval for μ if thesample size, n, is 20. How does decreasing the level of confidenceaffect the margin of error, E?

e)If the population had not been normally distributedcould we have computed the confidence intervals in parts (b) –(d)?

Answer & Explanation Solved by verified expert
3.5 Ratings (443 Votes)
aGivenPopulation mean 50Sampling distributon of Sample Mean Sample size n 20Standard deviation s 8Confidence intervalin 98bRequired confidence interval 50045428    See Answer
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