7.2-8.2

The values assigned to a population parameter based on the value(s) of a sample statistic are:

estimate(s)

Briefly explain the meaning of an estimator and an estimate.

An estimator is a sample statistic used to estimate a population parameter, while an estimate is the value(s) assigned to a population parameter based on the value of a sample statistic.

What is part of the procedure for estimating the value of a population parameter?

Collecting the required information from the members of the sample Selecting a sample Calculating the value of the sample statistic

You report a 95% confidence interval for a proportion as 53% ± 4%. Choose the most accurate statement below.

If you did this many times, 95% of those times, the true population proportion would be within your confidence interval.

What is the process of estimation?

Taking the value of a statistic and using it to estimate the value of a parameter.

A population has a distribution that is skewed to the left. Indicate whether the central limit theorem will apply to describe the sampling distribution of the sample mean of size n = 400

The central limit theorem can be applied.

Indicate whether the central limit theorem will apply to describe the sampling distribution of the sample proportion. n = 400 and p = .29

The central limit theorem can be applied.

Indicate whether the central limit theorem will apply to describe the sampling distribution of the sample proportion. n = 18 p = .25

The central limit theorem cannot be applied.

A population has a distribution that is skewed to the right. A sample of size is selected from this population. Describe the shape of the sampling distribution of the sample mean for the following case.

The distribution is slightly skewed to the right.

Explain the meaning of a point estimate and an interval estimate.

The value of a sample statistic used to estimate a population parameter is called a point estimate. In interval estimation, an interval is constructed around the point estimate, and it is stated that this interval is likely to contain the corresponding population parameter.

A parameter is a characteristic or measurement of a population. True or False

True

A statistics is a characteristic or measurement of a sample. True or False

True

The mean of the sampling distribution of the sample mean is:

always equal to the population mean

If the population from which samples are drawn is normally distributed, then the sampling distribution of the sample mean is:

always normally distributed

If the population from which samples are drawn is not normally distributed, then the sampling distribution of the sample mean is:

approximately normally distributed if n is 30 or larger

If (n/N) is less than or equal to 0.05, the standard deviation of the sampling distribution of the sample mean is equal to the population standard deviation:

divided by the square root of the sample size

The sample statistic used to estimate a population parameter is a(n):

estimator

For most distributions, we can use the normal distribution to make a confidence interval for a population mean provided that the population standard deviation is known and the sample size is:

greater than or equal to 30

To decrease the width of a confidence interval, we should always prefer to:

increase the sample size

You can decrease the width of a confidence interval by:

lowering the confidence level or increasing the sample size

The width of a confidence interval depends on the size of the:

margin of error

According to the Central Limit Theorem, the sampling distribution of the sample mean is approximately normal, irrespective of the shape of the population distribution, if:

n is 30 or larger

In the case of proportion, the sample size is large if:

np and nq are both greater than 5

The sampling distribution of the sample proportion is approximately normal if:

np and nq are both greater than 5

The single value of a sample statistic that we assign to the population parameter is a:

point estimate

Estimation is a procedure by which we assign a numerical value or numerical values to the:

population parameter based on the information collected from a sample

If you divide the number of elements in a population with a specific characteristic by the total number of elements in the population, the dividend is the population:

proportion

The mean of the sampling distribution of the sample proportion is equal to the population:

proportion

If you divide the number of elements in a sample with a specific characteristic by the total number of elements in the sample, the dividend is the:

sample proportion

When the sample size is greater than 1, the standard deviation of the sampling distribution of the sample means is always:

smaller than the standard deviation of the population

The mean of the sampling distribution of the sample mean is the mean of:

the means of all possible samples of the same size taken from the population

The standard deviation of the sampling distribution of the sample proportion is equal to:

the square root of pq/n

The margin of error for the population mean, assuming sd is known, is:

z multiplied by the standard deviation of the sample mean