Stats Exam Ch. 7 & 8

AAA batteries are advertised to have life of about 9 hours of use. With a certain level of confidence, it is advertised that the life is between 8-10 hours. if 9 hours is the point estimate, then the margin of error is

1 hour difference between 9 and 10

Sample means or sample proportions being monitored by using a control chart should lie

Between the upper and lower control limits.

chance variation

Caused by a number of randomly occurring events that are part of the production process

When a sample statistic is used to make inferences about a population parameter, it is referred to as a/an

Estimator

True or False: a parameter is a numerical measure that describes a sample.

False, A a parameter is a numerical measure that describes a POPULATION.

Control Chart

It is a plot of calculated statistics of a production process over time.

A firm uses acceptance sampling when

It produces a product and at the end of the process, inspects a portion.

The further a population proportion deviates from p= 0.50, the ____ the sample size required in order to satisfy a normal approximation.

Larger

The value of the finite population correlation factor is always

Less than one

If the shape of the population from which a simple random sample is drawn is normal, then the shape of the sampling distribution of |x is

Normal

In order to construct a confidence interval for U, the sampling distribution of the estimator |X must follow or approximately follow a(n) _____ distribution.

Normal

Parameter- Statistic- Estimate-

Parameter- constant Statistic- random variable Estimate- a particular value of an estimator

When estimating the population mean, the t_ df distribution is used when the

Population variance is unknown

The expected value of |P is the

Proportion of successes in the population

The mean and standard deviation are often used to described _____ data while the proportion is a descriptive measure that can be used for _____data.

Quantitative,Qualitative

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

Sampling distribution of |x

assignable variation is caused by

Specific events that can usually be identified and eliminated

True or False: The t_df distributions has slightly broader tails than the z distribution

True

The expected value of |X is equal to

U, because |X is unbiased

The Greek letter _____ denotes the level of significance.

a=Alpha

We use the finite population correction factor to

reduce the sampling variation of X and |P

For an |X chart, control limits are calculated as

u+_3*(o'/square root of n)

As a general guideline, the normal distribution approximation can be used to described the sampling distribution of the sample mean when

n >_ 30

We can use the finite population correction factor when

n>_ 0.05N

Population

It consists of all items of interest in a statistical problem, whereas a sample is a subset of the population.

The estimator |X follows a normal distribution when the underlying population follows a _____ distribution.

Normal

Bias

The tendency of a sample statistic to systematically overestimate or underestimate a population parameter.

True or False: A 95% confidence interval for U implies that if numerous samples are taken from a population, 95% of the intervals will contain U.

True

True or False: For a given sample size n and population standard o', the lower the confidence level 100(1-a)%, the narrower the confidence interval.

True

If a equals 0.01, when the confidence coefficient equals

(1-0.01)=0.99

What is the confidence level if a = 0.10?

(1-0.10)=0.90 Answer is 90%

A 95% confidence interval for the population proportion is calculated as (40, 80). The point of estimate for this interval is

(40+80)/2=60 Answer=0.60 or 60%

95% confidence interval for the population mean is calculated as (40, 80). The point of estimate for this interval is

(40+80)/2=60 answer is 60

Sample statistic

A random variable used to estimate the unknown population parameter of interest.

Non-response bias

A systematic difference in preferences between respondents and non-respondents to a survey or a poll.

Selection bias

A systematic under representation of certain groups from consideration for a sample.

In a statistical problem, a population consists of

All items of interest.

A theorem that allows us to use the normal probability distribution to approximate the sampling distribution of the sample mean whenever the sample size is large is known as the

Central limit theorem

random samples of size 400 are taken from a population whose population proportion is 0.25. The expected value of the sample proportion is

E(|P)=p=0.25

Stratified sampling is preferred to cluster sampling when the objective is to

Increase precision

Only way to reduce the margin of error is to

Increase the sample size

The branch of statistics that uses samples to estimate a population parameter or test a hypothesis about such a parameter is BEST referred to as______.

Inferential statistics

Whenever we construct a confidence interval for the population mean, the margin or error includes the standard error of |X and the

desired level of confidence

cluster sampling

the population is first divided up into mutually exclusive and collectively exhaustive groups, called clusters. A cluster sample includes observations from randomly selected clusters.

stratified random sampling

the population is first divided up into mutually exclusive and collectively exhaustive groups, called strata. A stratified sample includes randomly selected observations from each stratum. The number of observations per stratum is proportional to the stratum's size in the population. The data for each stratum are eventually pooled.

A random sample of 80 observations results in 50 successes. the point estimate of the population proportion of successes is

z_50/80=0.625

True or false: chance variation is not usually under the control of an individual worker or machine

True, Assignable variation is the type of variation that can be controlled.

True or False: If we had access to data that included the entire population, then the values of the parameters would be known and no statistical inference would be required.

True, If you have access to data that described the entire population, then the answers are perfect and no sampling or estimation is needed.

each t distribution is identified by its

degrees of freedom

How does an interval estimator differ from a point estimator?

interval estimator provides a range of values for the population parameter whereas a point estimator provides a single value.

All of the following are components of the formula for selecting n to estimate p EXCEPT:

^o'

A 95% confidence interval for the population mean is constructed as 6 +_ 2. what is the probability of error, a?

(1-0.95)=0.05 Answer is 0.05

The confidence coefficient equals

(1-a)

In general, the control limits of a control chart are set at ____ standard deviations from the center line.

3, it captures almost the entire bell curve.

When a firm applies statistical techniques to develop and maintain its ability to produce high-quality goods and services, it is implementing statistical_____.

Quality control

A confidence interval narrows if

The chosen confidence level decreases and the sample size increase.

The standard deviation of the sample mean The expected value of the sample mean The variance of the sample mean

The standard deviation of the sample mean- o'/square root of n The expected value of the sample mean- u The variance of the sample mean- o'^2/n

Sample

a subset of the population

simple random sample

is a sample of n observations that has the same probability of being selected from the population as any other sample of n observations.