Confidence Intervals for Means: The Basics

A confidence interval is centered around...

• a parameter

• a statistic

• the sample size

• the population size

Tags

CCSS.HSS.IC.A.1

CCSS.HSS.IC.B.4

 $\mu_{\overline{x}}=$  

•  $\mu_x$  

•  $\frac{\mu_x}{n}$  

•  $\frac{\mu_x}{\sqrt{n}}$  

•  $\sigma_x$  

Tags

CCSS.HSS.IC.A.1

CCSS.HSS.IC.B.4

 $\sigma_{\overline{x}}=$  

•  $\mu_x$  

•  $\frac{\sigma_x}{n}$  

•  $\frac{\sigma_x}{\sqrt{n}}$  

•  $\sigma_x$  

Tags

CCSS.HSS.IC.A.1

CCSS.HSS.IC.B.4

CCSS.HSS.ID.A.4

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

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

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

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.A.1

CCSS.HSS.IC.B.4

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

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

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