Chapter 6: 60E (page 363)

If you wish to estimate a population mean with a sampling error of SE = .3 using a 95% confidence interval, and you know from prior sampling that $σ^{2}$ is approximately equal to 7.2, how many observations would have to be included in your sample?

Short Answer

Expert verified

Sample of size n=18 observations Is required.

Step by step solution

Given information

The sampling error is 0.3, level of significance is 5% and $σ^{2} = 7.2$ .

Finding the sample size

$SE = 0.3, α = 0.05, and σ^{2} = 7.2$

The standard deviation is,

$\begin{array}{rcl} σ & = & \sqrt{7.2} \\ = & 2.6833 \end{array}$

The sample size required obtained by,

$\begin{array}{rcl} z_{\frac{α}{2}} (\frac{σ}{\sqrt{n}}) & = & SE \\ n & = & {[\frac{(z_{\frac{α}{2}}) σ}{SE}]}^{2} \\ n & = & [\frac{z_{0.025} \times 2.6833}{0.3}] \\ n & = & [\frac{1.960 \times 2.6833}{0.3}] [From Standard Normal Table] \\ n & = & \frac{5.2593}{0.3} \\ n & = & 17.531 \\ n & \approx & 18 \end{array}$

Therefore, 18 observations have to be included in the sample.

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If you wish to estimate a population mean with a sampling error of SE = .3 using a 95% confidence interval, and you know from prior sampling that $σ^{2}$ is approximately equal to 7.2, how many observations would have to be included in your sample?

Short Answer

Step by step solution

Given information

Finding the sample size

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If you wish to estimate a population mean with a sampling error of SE = .3 using a 95% confidence interval, and you know from prior sampling that σ2is approximately equal to 7.2, how many observations would have to be included in your sample?

Short Answer

Step by step solution

Given information

Finding the sample size

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Decision Maths

Mechanics Maths

Discrete Mathematics

Calculus

Statistics

Applied Mathematics

Study anywhere. Anytime. Across all devices.

If you wish to estimate a population mean with a sampling error of SE = .3 using a 95% confidence interval, and you know from prior sampling that $σ^{2}$ is approximately equal to 7.2, how many observations would have to be included in your sample?