chpt. 5-8 stats exam vocab

as the degrees of freedom go to infinity, the t distribution converges to the z distribution and both have asymptotic tails—that is, their tails become closer and closer to the horizontal axis but never touch it

The tdf distribution is similar to the z distribution because ___________________________________________.

normal

To construct a 95% confidence interval for µ, the sampling distribution of X⎯⎯⎯ must be _______.

Is constant for all x between a and b, and 0 otherwise.

A continuous random variable has the uniform distribution on the interval [a, b] if its probability density function f(x) _______.

narrower;wider

A sample of a given size is used to construct a 95% confidence interval for the population mean with a known population standard deviation. If a bigger sample had been used instead, then the 95% confidence interval would have been _______ and the probability of making an error would have been ________.

if sample size is n > 30

According to the central limit theorem, the distribution of the sample means is normal if _______.

Use the z table when σ is known; use the t table when σ is unknown.

Confidence intervals of the population mean may be created for the cases when the population standard deviation is known or unknown. How are these two cases treated differently?

It is smaller and therefore suggests that averages have less variation than individual observations.q

How does the variance of the sample mean compare to the variance of the population?

standard

If X⎯⎯⎯ is normally distributed then we can transform it into a(n) _______ normal random variable.

For any sample size n, the sampling distribution of the sample mean is normally distributed.

If a population is known to be normally distributed, what can be said of the sampling distribution of the sample mean drawn from this population?

round up

If calculated required sample size is a noninteger value, we should always _______ calculated value.

all the above

Let X be normally distributed with mean μ and standard deviation σ > 0. Which of the following is true about the z value corresponding to a given x value? A positive z = (x - μ)/σ indicates how many standard deviations x is above μ. A negative z = (x - μ)/σ indicates how many standard deviations x is below μ. The z value corresponding to x = μ is zero. All of the above.

is closer to a normal distribution

The central limit theorem states that, for any distribution, as n gets larger, the sampling distribution of the sample mean _______.

1/(b - a) between a and b, and zero otherwise.

The height of the probability density function f(x) of the uniform distribution defined on the interval [a, b] is _______.

proportion

The parameter p represents the ________ of successes in the population.

.5

The probability that a normal random variable is less than its mean is _______.

A statistic is a random variable.

Which of the following is true about statistics such as the sample mean or sample proportion?

wider; smaller

A 90% confidence interval is constructed for the population mean. If a 95% confidence interval had been constructed instead (everything else remaining the same), the width of the interval would have been ________ and the probability of making an error would have been _________.

estimate

Statistics are used to estimate population parameters, particularly when it is impossible or too expensive to poll an entire population. A particular value of a statistic is referred to as a(n) ______

expected value

The _______ _____ of X⎯⎯⎯ is the same as the mean of the individual observations.

confidence

The ________ coefficient is equal to 1- α .

0≤P(X = x)≤1 and ∑P (X = xi ) = 1

What are the two key properties of a discrete probability distribution?

The underlying population need not be normally distributed if the sample size is 30 or more.

What conditions are required by the central limit theorem before a confidence interval of the population mean may be created?

The tails get closer and closer to the x axis but never touch it.

What does it mean when we say that the tails of the normal curve are asymptotic to the x axis?

point estimate +/- margin of error

What is the most typical form of a calculated confidence interval?

To provide a range of values that, with a certain measure of confidence, contains the population parameter of interest.

What is the purpose of calculating a confidence interval?

normally of the estimator

Which of the following is the necessary condition for creating confidence intervals for the population mean?

The tdf distribution has broader tails (it is flatter around zero).

How do the tdf and z distributions differ?

If the sample size is bigger, the interval is narrower.

For a given confidence level and population standard deviation, which of the following is true in the interval estimation of the population mean?

If the population standard deviation is greater, the interval is wider.

For a given confidence level and sample size, which of the following is true in the interval estimation of the population mean when σ is known?

If the confidence level is greater, the interval is wider.

For a given sample size and population standard deviation, which of the following is true in the interval estimation of the population mean?

normally

For making statistical inferences, it is essential that the sampling distribution of X⎯⎯⎯ is _________ distributed.