A random sample is drawn from a population with 12 The sample mean is 30 (a) Compute a 95 confidence interval for based on a sample of size 49 What is the value of the margin of error (b) Compute a 95 confidence interval for based on a sample of size 100 What is the value of the margin of error (c) Compute a 95 confidence interval for based on a sample of size 225 What is the value of the margin of error (d) Compare the margins of error for parts (a)(c) As the sample size increases, does the margin of error decrease (e) Compare the lengths of the confidence intervals for parts (a)(c) As the sample size increases, does the length of a 90 confidence interval decrease

Question: A random sample is drawn from a population with = 12. The sample mean is 30. (a) Compute a 95% confidence interval for

A random sample is drawn from a population with σ = 12. The sample mean is 30.
(a) Compute a 95% confidence interval for μ based on a sample of size 49. What is the value of the margin of error?
(b) Compute a 95% confidence interval for μ based on a sample of size 100. What is the value of the margin of error?
(c) Compute a 95% confidence interval for μ based on a sample of size 225. What is the value of the margin of error?
(d) Compare the margins of error for parts (a)–(c). As the sample size increases, does the margin of error decrease?
(e) Compare the lengths of the confidence intervals for parts (a)–(c). As the sample size increases, does the length of a 90% confidence interval decrease?

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