Central Limit Theorem - Confidence Level and Sample Size

#1
Answer the following based upon the implications of the Central Limit Theorem (assume sample size larger than 30 when samples are mentioned in (a) and (b) below).

a) How does the mean of the sampling distribution of all possible sample means from a population compare to the mean of the population?

b) How does the standard deviation of the sampling distribution of all possible sample means from a population compare to the standard deviation of the population.

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#2
Suppose you want to estimate the percentage of all voters across the nation who voted for Obama in the Democratic party primaries and you want your estimate to be within 3 percentage points of the correct population measure, based upon a 90% confidence level. What size sample is required? (assume that no estimate of p-hat is known)

Solution Preview

(1) (a) As the sample size increases (and for sample size > 30) the mean of the sampling distribution of the means equals (or very closely approaches) the population mean.

(b) As ...

Solution Summary

Two questions on Central Limit Theorem - Confidence Level and Sample Size solved.

... 95% confidence interval for the population proportion is given ... The central limit theorem states that given a distribution ... σ²/N as the sample size N increases ...

... A 95% confidence interval or a 99% confidence interval? ... The central limit theorem also shows that given a ... of the standard deviation of each individual sample. ...

... the required calculations for the confidence interval and necessary ... a) Point #1 The central limit theorem states that ... b) Point #2 As the sample size N increases ...

... thus the result predicted by central limit theorem is true ... Is the histogram icted by the Central 37.39 - 39.24 ...Confidence Area in Two Sample Level Tails Size 90 ...

... (a) Construct a 95 percent confidence interval for the ... larger improves as N ". The Central Limit Theorem predicts that ... When the sample size increases we can be ...

... the lower limit of the confidence interval is 49.05 ... the Central Limit Theorem: The central limit theorem states that ... large enough As the sample size gets large ...

Normal Distribution and Central Limit Theorem. ... Z at the 0.1 level of significance 2 tails = 1.6449. Upper confidence limit= M +z*sx= 24.6631 =23.5+1.6449*0.7071 ...

... Answer: The central limit theorem is of crucial importance in ... Answer: In general a 95% confidence interval is interpreted ... are taken and their sample means are ...

... Why not use other confidence levels? ... The interesting thing about the central limit theorem is that no ... deviation of the distribution of the sample mean over ...

... (a) Construct a 95 percent confidence interval for the ... The central limit theorem states that given a distribution with a ... σ²/N as N, the sample size, increases ...