Ch 6 - Statistical Inference

For the 99% confidence interval, what is a/2?

0.005

Often it is more informative to provide a range of values - an interval - rather than a single point estimate for the unknown population parameter. What two terms are used for this range of values called?

1. Interval estimate 2. Confidence interval

Which of the following is true of the population proportion p?

1. Is a descriptive measure for a qualitative variable 2. It is estimated on the basis of its sample counterpart, the sample proportion ̄P

Which of the following is true of the Central Limit Theorem?

1. It requires a sample size of approximately 30. 2. It is used to approximate normal distributions.

Which of the following summarizes the two correct decisions related to Type I and Type II errors?

1. Rejecting the null hypothesis when the null hypothesis is false 2. Not rejecting the null hypothesis when the null hypothesis is true

The sampling distribution of P is closely related to which distribution?

Binomial

Which of the following is an example of a Type II Error?

Can occur when the null hypothesis is false

There is only one population, but many possible samples of a given size can be drawn from the population. Which of the following is a constant, even though its value may be unknown?

Population Parameter

If sample evidence is inconsistent with the null hypothesis, we ___ the null hypothesis.

Reject

Another standardized statistic, which uses the estimator S in place of σ, is computed as T= ̄X−μ/S/√n. Which distribution does the random variable T follow?

T distribution

What is a requirement for two sample means in order to conduct a hypothesis test for the difference between the two means? Select all that apply!

The means must be from independent random samples

Confidence interval

provides a range of values that, with a certain level of confidence, contains the population parameter of interest.

The standard error of the sample mean equals:

the population standard deviation divided by the square root of the sample size.

Margin of error accounts for:

the standard error of the estimator and the desired confidence level of the interval.

The basic principle of hypothesis testing is to first assume that the null hypothesis is ___ and then determined if sample evidence contradicts this assumption.

true

An estimator is ___ if its expected value equals the population parameter of interest.

unbiased

The first type of matched-pairs sample is characterized by a measurement, an intervention of some type, and then another measurement. We generally refer to these experiments as:

"Before" and "after" studies.

In a sample of 25 ultra-green cars, seven of the cars obtained over 100 miles per gallon (mpg). Match the following for the construct of a 90% confidence intervals for the population proportion of all ultra-green cars that obtain over 100 mpg

1. a/2 - 0.10/2 2. population proportion p bar - 7/25 = 0.28 3. z - 1.645 4. Lower end of confidence interval - 13.2% 5. Upper end of confidence interval - 42.8%

We use hypothesis testing to resolve conflicts between two competing hypotheses on a particular population parameter of interest. Which of the following corresponds to the null hypothesis?

1. denoted H0 2. corresponding to a presumed default state of nature or status quo

An ___ is ___ if its expected value equals the population parameter of interest.

1. estimator 2. unbiased

Order the steps in developing a hypothesis in order from the first to second to third step.

Choice 1 of 3. Identify the relevant population parameter of interest toggle button Identify the relevant population parameter of interest Choice 2 of 3. Determine whether it is a one- or two-tailed test. toggle button Determine whether it is a one- or two-tailed test. Choice 3 of 3. Include some form of the equality sign in the null hypothesis and use the alternative hypothesis to establish a claim. toggle button Include some form of the equality sign in the null hypothesis and use the alternative hypothesis to establish a claim.

We are conducting a hypothesis test using α = 0.05. H0:Do not build brick-and-mortar store. HA:Build brick-and-mortar store. We determine that the p-value is .20. What is our decision?

Do not reject the null hypothesis

The expected value of the sample mean X equals the population mean; that is,

E (X (sample mean)) = mew

The chefs at a local pizza chain in Cambria, California, strive to maintain the suggested size of their 16-inch pizzas. Despite their best efforts, they are unable to make every pizza exactly 16 inches in diameter. The manager has determined that the size of the pizzas is normally distributed with a mean of 16 inches and a standard deviation of 0.8 inch. What are the expected value and the standard error of the sample mean derived from a random sample of 2 pizzas?

E(X) = 16 and se(X (sample mean))= 0.8/√2 = 0.57

Which of the following is a correct null hypothesis for the difference between two means?

H0: μ1 − μ2 ≥ d0

A confidence interval is generally associated with a ___ ___ ___

Margin of error

What is the term used in a confidence interval that accounts for the standard error of the estimator and the desired confidence level of the interval?

Margin of error

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

Normally

Sample proportion is represented as

P with a line on top.

Recall that the population proportion p is the essential descriptive measure for a qualitative variable, and that it is estimated on the basis of its sample counterpart. What is its sample counterpart?

The sample proportion ̄P

True or false: In most applications, we require some form of the equality sign in the null hypothesis

True

True or false: The expected value of the sample proportion P is equal to the population; that is E(P) = p

True

The variance of X(mean) is equal to

Var (X (mean)) = Sigma squared / n

The second type of matched-pairs sample is characterized by a pairing of observations, which means:

Where it is not the same individual who gets sampled twice

The degrees of freedom determine the extent of the broadness of the tails of the distribution; if there are fewer degrees of freedom, the tail of the distribution is more:

broad

A particular value of the estimator is called an ___.

estimate

When a statistic is used to estimate a parameter, it is referred to as an ___.

estimator

For making statistical inferences, it is essential that the sampling distribution of X (sample mean) is ___ distributed.

normally

Population proportion is represented as

p

Particular value (estimate) is denoted by

p with a line on top

A population ___ is a constant, even though its value may be unknown.

parameter

The standard error is calculated as:

se (X(sample mean)) = Sigma / the square root of n

We refer to the standard deviation of X(sample mean) as the ___ ___ of the sample mean.

standard error

A ___ is a variable whose value depends on the particular sample that is randomly drawn from the population (random sample).

statistic