SB 8.1-8.2

The standard deviation of the sampling distribution of xx is equal to

__ σX=σ/√n

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

closer to a normal distribution.

The expected value of p̂ is the

proportion of successes in the population.

A list of all possible values of the sample mean and the probabilities of these values being observed is known as the ______.

sampling distribution of x(bar)

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.

The shape of the sampling distribution of p̂ becomes more normal as _________

the sample size increases.

The probability distribution describing the set of all possible values of s^2 is called

the sampling distribution of s^2.

Suppose we find that if a population proportion is 0.72, the chance of seeing a sample proportion that is less than or equal to 0.70 is 0.1251. If we observe p̂= 0.70,

we have insufficient evidence to doubt that p = 0.72.

You discover that if μ =10, then the probability of observing x(bar) ≤ 8.8 is 0.0034. Your observed value of x(bar) = 8.8. What do you conclude?

μ < 10

The standard deviation of p̂ equals

√p(1−p)/n

Consider a population having mean μ =100. If μ̂ is an unbiased point estimate of μ, then the mean of μ̂ is

100

A population has a mean of 100 and a standard deviation of 12. A random sample of 36 is selected. The standard deviation __ of x is equal to

2

The central limit theorem states that the distribution of the sample mean will be approximately normal if the sample size is sufficiently large; as a general guideline n≥ ___________.

30

Consider a population having mean μ = 100 and variance σ2 = 36. Given that s2 is an unbiased estimate of σ2, the mean value of s2 must be

36

If the variability between individual observations of a population is equal to 10, which of the following is a possible value for the variability between the values of the sample mean?

8

If we assume that a population has proportion p = 0.2 and we choose a random sample of size 400, what is the chance the sample proportion pˆ is greater than or equal to 0.25?

0.0062

Suppose we choose a sample of size 100 from a population of monthly cable bills having standard deviation $20. If we assume the population mean bill is $65, what is the probability mean of our sample is greater than $70?

0.0062

Suppose you choose a sample of size 100 from a population having 25% successes. The sample proportion of successes will have standard deviation

0.0433

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

0.25

A population has a mean of 50 and a standard deviation of 10. A random sample of 256 is selected. The standard deviation of x(bar) is equal to

0.625

Suppose a population consists of many copies of the numbers 1, 2, and 3. If you choose a sample of size 2, what are the possible values of the sample mean?

1, 1.5, 2, 2.5, 3

The sampling distribution of the sample mean is _____

likely to look more similar to a normal curve than the population distribution does.

In many situations, the distribution of the population of all possible sample means looks like a

normal curve.

For any population proportion p, the sampling distribution of the sample proportion is approximately normally distributed if

np ≥5 and n(1 - p) ≥5.

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

n≥30.

The sampling distribution of the sample median tells us about the set of all possible values

of the sample median.