μ x ‾ = \mu_{\overline{x}}= μ x =

μ x n \frac{\mu_x}{\sqrt{n}} n <path d="M95,702c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5, -10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8, -50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0, 35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5, -221c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467 s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422 s-65,47,-65,47z M834 80H400000v40H845z"> μ x

σ x ‾ = \sigma_{\overline{x}}= σ x =

σ x n \frac{\sigma_x}{\sqrt{n}} n <path d="M95,702c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5, -10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8, -50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0, 35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5, -221c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467 s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422 s-65,47,-65,47z M834 80H400000v40H845z"> σ x

σ x n \frac{\sigma_x}{n} n σ x

Which expression correctly gives the area in each tail when the confidence interval c c c is expressed as a decimal?

1 − c 2 \frac{1-c}{2} 2 1 − c

c − 1 2 \frac{c-1}{2} 2 c − 1

Which of the following are correct formulas for finding the margin of error for a sampling distribution with a sample size of 50? Check all that apply.

E = z c σ x ‾ E=z_c\sigma_{\overline{x}} E = z c σ x

E = z c ⋅ σ x n E=z_c\cdot\frac{\sigma_x}{\sqrt{n}} E = z c ⋅ n <path d="M95,702c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5, -10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8, -50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0, 35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5, -221c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467 s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422 s-65,47,-65,47z M834 80H400000v40H845z"> σ x

E = x ‾ + z c σ E=\overline{x}+z_c\sigma E = x + z c σ

E = z c ⋅ σ x n E=z_c\cdot\frac{\sigma_x}{n} E = z c ⋅ n σ x

E = t c ⋅ s n E=t_c\cdot\frac{s}{\sqrt{n}} E = t c ⋅ n <path d="M95,702c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5, -10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8, -50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0, 35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5, -221c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467 s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422 s-65,47,-65,47z M834 80H400000v40H845z"> s

Which of the following are correct formulas for finding the margin of error for an approximately normal sampling distribution with a sample size of 20 and an unknown \sigma σ ? Check all that apply.

E = t c ⋅ s n E=t_c\cdot\frac{s}{\sqrt{n}} E = t c ⋅ n <path d="M95,702c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5, -10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8, -50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0, 35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5, -221c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467 s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422 s-65,47,-65,47z M834 80H400000v40H845z"> s

E = x ‾ + t c σ E=\overline{x}+t_c\sigma E = x + t c σ

E = z c σ x ‾ E=z_c\sigma_{\overline{x}} E = z c σ x

E = z c ⋅ σ x n E=z_c\cdot\frac{\sigma_x}{n} E = z c ⋅ n σ x

E = z c ⋅ σ x n E=z_c\cdot\frac{\sigma_x}{\sqrt{n}} E = z c ⋅ n <path d="M95,702c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5, -10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8, -50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0, 35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5, -221c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467 s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422 s-65,47,-65,47z M834 80H400000v40H845z"> σ x

n \sqrt{n} n <path d="M95,702c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5, -10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8, -50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0, 35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5, -221c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467 s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422 s-65,47,-65,47z M834 80H400000v40H845z">

n − 1 \sqrt{n-1} n − 1 <path d="M95,702c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5, -10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8, -50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0, 35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5, -221c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467 s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422 s-65,47,-65,47z M834 80H400000v40H845z">

We cannot use either the Normal Distribution or the t t t -distribution as models for our sampling distribution when _______________________ AND _______________________ .

the data distribution is NOT approximately normal

Resource Library

Math

The Basics

Confidence Intervals For Means: The Basics

Confidence Intervals for Means: The Basics

Authored by Matthew Kilgore

Mathematics

11th Grade - University

CCSS covered

Used 37+ times

Confidence Intervals for Means: The Basics

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25 questions

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MULTIPLE CHOICE QUESTION

15 mins • 1 pt

A confidence interval is centered around...

a parameter

a statistic

the sample size

the population size

Tags

CCSS.HSS.IC.B.4

CCSS.HSS.IC.A.1

MULTIPLE CHOICE QUESTION

15 mins • 1 pt

$\mu_{\overline{x}}=$

$\mu_x$

$\frac{\mu_x}{n}$

$\frac{\mu_x}{\sqrt{n}}$

$\sigma_x$

Tags

CCSS.HSS.IC.B.4

CCSS.HSS.IC.A.1

MULTIPLE CHOICE QUESTION

15 mins • 1 pt

$\sigma_{\overline{x}}=$

$\mu_x$

$\frac{\sigma_x}{n}$

$\frac{\sigma_x}{\sqrt{n}}$

$\sigma_x$

Tags

CCSS.HSS.ID.A.4

CCSS.HSS.IC.B.4

CCSS.HSS.IC.A.1

MULTIPLE CHOICE QUESTION

15 mins • 1 pt

What is a sampling distribution of means?

The collection of all possible sample means and their associated probabilities.

The collection of all possible sample means of a given sample size and their associated probabilities.

The collection of all possible population means and their associated probabilities.

The collection of all possible population means of a given population size and their associated probabilities.

Tags

CCSS.HSS.MD.A.1

CCSS.HSS.MD.A.2

CCSS.HSS.MD.A.3

MULTIPLE SELECT QUESTION

15 mins • 1 pt

Which of these conditions are sufficient to assume that a sampling distribution is approximately normal? Check all that apply.

When the data distribution is approximately normal and $\sigma$ is known

When the sample size is at least 30

When the population standard deviation is known

When the original data distribution is approximately symmetric

Tags

CCSS.HSS.ID.A.2

CCSS.HSS.ID.A.3

MULTIPLE SELECT QUESTION

15 mins • 1 pt

Which of these conditions are necessary in order for the best model for the sample distribution to be a $t$ -distribution? Check all that apply.

The sample size is at least 30

The sample size is less than 30

The original data distribution is approximately normal

The population standard deviation is known

The population standard deviation is unknown

MULTIPLE CHOICE QUESTION

15 mins • 1 pt

When we say we have a 90% confidence interval, what are we 90% confident of?

That the population mean is within the interval boundaries

That the population mean is outside the interval boundaries

That the sample mean is within the interval boundaries

That the sample mean is outside the interval boundaries

Tags

CCSS.HSS.IC.B.4

CCSS.HSS.IC.A.1

MULTIPLE CHOICE QUESTION

15 mins • 1 pt

What are the critical z-values for a 80% confidence interval?

$\pm1.28$

$\pm1.645$

$\pm1.96$

$\pm2.575$

Tags

CCSS.HSS.ID.A.4

MULTIPLE CHOICE QUESTION

15 mins • 1 pt

What are the critical z-values for a 90% confidence interval?

$\pm1.28$

$\pm1.645$

$\pm1.96$

$\pm2.575$

Tags

CCSS.HSS.ID.A.4

10.

MULTIPLE CHOICE QUESTION

15 mins • 1 pt

What are the critical z-values for a 95% confidence interval?

$\pm1.28$

$\pm1.645$

$\pm1.96$

$\pm2.575$

Tags

CCSS.HSS.ID.A.4

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Confidence Intervals for Means: The Basics

A confidence interval is centered around...

μx‾=\mu_{\overline{x}}=μx​=

σx‾=\sigma_{\overline{x}}=σx​=

What is a sampling distribution of means?

Which of these conditions are sufficient to assume that a sampling distribution is approximately normal? Check all that apply.

Which of these conditions are necessary in order for the best model for the sample distribution to be a ttt -distribution? Check all that apply.

When we say we have a 90% confidence interval, what are we 90% confident of?

What are the critical z-values for a 80% confidence interval?

What are the critical z-values for a 90% confidence interval?

What are the critical z-values for a 95% confidence interval?

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$\mu_{\overline{x}}=$

$\sigma_{\overline{x}}=$

Which of these conditions are necessary in order for the best model for the sample distribution to be a $t$ -distribution? Check all that apply.