DS 23 TEST #3

About what percent of the area under the normal curve is within plus two and minus two standard deviation of the mean?

95% (95.5%)

The standard normal probability distribution is one which has

A mean of 0 and a standard deviation of 1

As the size of the sample increases, what happens to the shape of the sampling distribution of sample means?

Approaches a normal distribution

All possible samples of size n are selected from a population and the mean of each sample is determined. What is the mean of the sample means?

Exactly the same as the population

The variation in the population as measured by the standard deviation has little or no effect in determining the size of a sample selected from the population.

False

To determine the value of the standard error of the mean, the total error is divided by the sample size.

False

One factor in determining the size of a sample is the maximum allowable error that you must decide on. It is the maximum error you will tolerate at a specified level of confidence.

True

The 95 percent confidence interval states that 95 percent of the sample means of a specified sample size selected from a population will lie within plus and minus 1.96 standard deviations of the hypothesized population mean.

True

The Central Limit Theorem states that if the sample size n is sufficiently large, the sampling distribution of the means will be approximately normal no matter whether the population is normally distributed, skewed, or uniform.

True

The Student t distribution has a greater spread than does the z distribution. As a result, the critical values of t for a given level of significance are larger in magnitude than the corresponding z critical values.

True

The area under the normal curve within plus and minus one standard deviation of the mean is about 68%.

True

The higher the degree of confidence, the larger the sample required to give a certain precision.

True

The mean divides the normal curve into two identical halves.

True

The normal curve falls off smoothly in either direction from the central value. Since it is asymptotic, the curve gets closer and closer to the X-axis, but never actually touches it.

True

The standard error of the mean will vary according to the size of the sample that is in the denominator. As the sample size n gets larger, the variability of the sample means gets smaller.

True

The standard normal distribution is a special normal distribution with a mean of 0 and a standard deviation of 1.

True

The t distribution is based on the assumption that the population of interest is normal or nearly normal.

True

The t distribution is more spread out and flatter at the center than is the standard normal distribution. However, as the sample size increases, the t distribution curve approaches the standard normal distribution.

True

The test statistic for a problem involving a small sample of under 30 and the population standard deviation is unknown is the Student's t distribution.

True

The test statistic t has n - 1 degrees of freedom.

True

The total area under the normal curve is 1.00.

True

There is not one t distribution, but rather a "family" of t distributions.

True

We can expect some difference between sample statistics and the corresponding population parameters. This difference is called the sampling error.

True

When referring to the normal probability function, there is not just one of them; there is a "family" of them.

True

What is the interval within which a population parameter is expected to lie?

confidence interval

The mean of all possible sample means is equal to the

population mean.

Sampling error is the difference between a sample statistic and the corresponding

population parameter.

A sample standard deviation is the best point estimate of the

population standard deviation

What proportion of the area under a normal curve is to the right of a z-score of zero?

50

For a standard normal distribution, what is the probability that z is greater than 1.75?

0.0401

What is the area under the normal curve between z = -1.0 and z = -2.0?

0.1359

What is the area under the normal curve between z = 0.0 and z = 1.79?

0.4633

What is the value of the continuity correction factor?

0.50

What proportion of the area under a normal curve is to the left of z = 0.50?

0.6914

What proportion of the area under a normal curve is to the right of z = -1.02?

0.8461

What sample statistic is used to estimate a population parameter?

Point estimate

What is NOT necessary to determine how large a sample to select from a population?

Size of the population

In what units does the standardized z value measures distance from the mean?

Standard deviation

A continuity correction compensates for estimating a discrete distribution with a continuous distribution.

True

A sampling distribution of the means is a probability distribution consisting of a list of all possible sample means of a given sample size selected from a population and the probability of occurrence associated with each sample mean.

True

A z-score is the distance between a selected value (X) and the population mean divided by the population standard deviation .

True

Asymptotic means that the normal curve gets closer and closer to the X-axis but never actually touches it.

True

Based on the sampling distribution of the means and the central limit theorem, the sample mean can be used as a good estimator of the population mean, assuming that the size of the sample is sufficiently large.

True

If a population is not normally distributed, the sampling distribution of the sample means tends to approximate a normal distribution if the sample size is large enough.

True

If the sample size keeps getting larger and larger and finally equals the size of the population, there would be no error in predicting the population mean because the sample size and the size of the population would be the same.

True

If the size of a sample equals the size of the population, we would not expect any error in estimating the population parameter.

True

One factor in determining the size of a sample is the degree of confidence selected. This is usually 0.95 or 0.99, but it may be any degree of confidence you specify.

True