# Statistics Questions Related to Sampling

What differentiates a z test statistic for a population from the z statistic for a sampling of means? Why the difference?

Consider a normal population with μ = 43 and σ = 5.2. Calculate the z-score for an x ̅ of 46.5 from a sample of size 16.

Find the critical value z a/2 that corresponds to the given confidence level. 88%

za/2=_____

Assume that a random sample is used to estimate a population p. Find the margin of error E that corresponds to the given statistics and confidence level. N=550, x=220, 90% confidence.

The margin of error E=____

Calculate the margin of error E=Za/2•ơ/√n

The confidence level is 99%, the sample size is n=103, and ơ=16

E=____

Salaries of 47 college graduates who took a statistics course in college have a mean, x ̅ of $65,000. Assuming a standard deviation ơ of $16,817, construct a 99% confidence interval for estimating the population mean µ.

$___< µ < $____

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#### Solution Preview

1. What differentiates a z test statistic for a population from the z statistic for a sampling of means? Why the difference?

If X is a normal variable with mean mu and sd sigma, then z statistic=(x-mu)/sigma. But if a sample of size n is drawn from a normal population with mean xbar and sd s, then z statistic

=(xbar-mu)/[s/sqrt(n)]. This is due to the different sample size.

2. Consider a normal ...

#### Solution Summary

The solution gived detailed steps on solving some questions on the topic of descriptive statistics. All formula and calculations are shown and explained.