Sampling Distributions and Estimation

The quick rule of three says that if a sample of 20 restaurant customers was asked if their meal was satisfactory and none replied yes, then the upper limit on the confidence interval for π would be

.15

The conservative assumption for π when conducting polls or survey research is

.50

For a 90% confidence interval the value for zα/2 is _____. (Round to three decimals.)

1.645

When applying the CLT to define an interval within which we expect 95% of all sample means to fall we would use a z = _______.

1.96

For a population with μ = 25 and σ = 5, we would expect 90% of all x's calculated from n = 35 to fall between _______ and ________

23.61 26.39

For a population with μ = 25 and σ = 5, we would expect 90% of all x's calculated from n = 35 to fall between _____ and _______

23.61 26.39

The normal distribution approximation for x is typically considered appropriate when the sample size n ≥

30

When constructing a confidence interval from a non-normal population with known variance, the common rule of thumb for sample size is that n ≥

30

The sample size required for a 95% confidence level to estimate μ with a margin of error = 2 and with σ = 6 is n =

35

The proportion calculated from a sample of size 50 is approximately normally distributed if x is between 10 and ___

40

The common confidence level used in polls is

95%

To find the t statistic for a 95% confidence level with n = 23 using Excel, type the following function:

=T.INV.2T(.05,22)

A 95% confidence interval implies that the probability that μ falls in that interval is 0.95.

False

A report states that the 90% confidence interval for the national average salary for a high school math teacher is $46,000 ± $4000. This means that

If a sample from a specific school district has an x = $40,000, we can conclude that this district has a lower average salary than the nation. We are 90% confident that the national average salary for high school math teachers is between $42,000 and $50,000

In which application would it be safe to assume that σ is known?

Quality Control studies

The sampling distribution of a sample mean refers to

The probability distribution of all x values calculated from all possible samples of size n.

For a given sample size n and population standard deviation σ, a lower confidence level implies a narrower confidence interval.

True

An interval within which we expect 95% of all x's to fall can be defined for any population by applying the

central limit theorem

Proportions are often easier to estimate than other parameters (such as a mean) because proportions arise from _________ things.

counting

If we want a more precise interval estimate for π we could

decrease the confidence level. increase the sample size

When constructing a confidence interval from a normal population the sample size

doesn't matter.

Some of the desirable properties of a point ______ include unbiasedness, consistency, and efficiency.

estimator

For a given confidence level and sample size, when σ is unknown, the confidence interval for μ will be _________ than if σ is known.

higher

If observations appear to be unusual or outliers one should

investigate to determine if the observations came from a different population. Investigate to determine if the data are in error. investigate to determine if the outliers are causing skewness.

For a given population proportion π, the sampling distribution for p is approximately normal when the following 2 requirements are satisfied:

n(1-π) ≥ 10 nπ ≥ 10

The t statistic should be used instead of z to estimate μ when the population ________ _________ is unknown.

standard deviation

An underlying assumption for using the t distribution is

that the population should have a normal distribution.

A sample size less than 30 might be sufficient for the sampling distribution on x to be considered approximately normal if

the population distribution is symmetric.

Using the t distribution when the population is NOT normal can provide reliable results as long as

the sample size is not too small. the population distribution is not badly skewed.

Each t distribution is dependent on

the size of the sample

The Rule of 3 for proportions applies when

there are no events in n trials.

It is rare that the population variance is known.

true

The three characteristics required to properly describe a sampling distribution are

variance shape mean

By increasing the sample size, n, and keeping the confidence level the same, the width of the confidence interval

will decrease

The equation for a confidence interval for μ when the population standard deviation is known is

X̄±Za/2 σ/√n

The margin of error in the formula for the confidence level of a population proportion is

Zα/2√p(1−p)n

A t distribution has

a symmetrical shape. slightly broader tails than the z distribution.

The confidence interval of for µ when σ is unknown will be wider than if σ were known because __________.

a t statistic will be greater than the z score for the same level of confidence. we have more uncertainty about the population when estimating σ with s.

Proportions frequently occur in surveys and are most often expressed as

percent's

The probability distribution of the sample mean is commonly referred to as the ______ distribution of the sample mean.

sampling