(7) Smartbook - Confidence Intervals

parameter

"A confidence interval is na interval or range of values that is used to estimate the value of a *_* such as the population mean.

p

"Symbol that represents the population proportion, which we can estimate using a confidence interval."

p hat

"Symbol that represents the sample proportion of individuals who are in a specified category."

margin of error

"The number that is added to and subtracted from the point estimate to create a confidence interval that is likely to contain a parameter such as the population mean is known as the *_ _ _*."

population, unlikely

"The value of x bar can be used as a point estimate for the *_* mean. However it is LIKELY or UNLIKELY to be equal to the value it is estimating."

critical

"We call the numbers on the horizontal axis of the standard normal curve that separate a middle percentage of area, such as 95%, from the rest of the area "*_* values". These are used to construct confidence intervals."

Assumptions for Constructing a Interval for p

1) We have a simple random sample. 2) The population is at least 20 times as large as the sample. 3) The items in the population are divided into two categories. 4) The sample must contain at least 10 individuals in each category.

margin

Once the assumptions to construct a confidence interval for μ when σ is known have been met, a confidence interval is created by finding the values of the sample mean plus or minus the *_* of error.

margin, critical

The *_* of error is the *_* value times the standard error of the sample means.

False

True or False: It is likely that the point estimate x bar is exactly equal to the population mean.

point estimate

What do these characteristics represent? - it is a single number. - it is used to estimate a parameter.

critical value x standard error

What is equal to the margin of error used to create a confidence interval for the population mean when σ is known?

Z(a/2)

What is the correct notation for the critical value when a random sample is selected from a normal population to construct a 1 - a confidence interval for μ(population mean) when σ(standard deviation) is known?

x + 2/n +4

If the assumption for constructing a confidence interval for a proportion requires at least 10 individuals in each category is not met... Adjusted sample proportion is *_ + _/ _+_*

2

If the assumption for constructing a confidence interval for a proportion requires at least 10 individuals in each category is not met... Increase the number of individuals in the category by *_*.

4

If the assumption for constructing a confidence interval for a proportion requires at least 10 individuals in each category is not met... Increase the sample size by *_*.

adjusted sample proportion

If the assumption for constructing a confidence interval for a proportion requires at least 10 individuals in each category is not met... Use an *_ _ _* in place of p hat.

up

If the value of n resulting from the formula is not a whole number, round it UP or DOWN to the next whole number.

0.5

If the value of p hat is NOT provided, what number value should you use?

decrease

If we decrease the level of confidence for a confidence interval and other components remained the same, then the margin of error will *_*.

large

In order to construct a confidence interval for μ when σ is known... If the distribution of the population is not approximately normal, then the sample size must be *_*.

approximately normal

In order to construct a confidence interval for μ when σ is known... If the sample size is not large, the the distribution of the population must be * _ _ *.

have

In order to construct a confidence interval for μ when σ is known... We HAVE or DON'T HAVE a simple random sample.

m

The variable in *_* in the formula represents the margin of error.