QMB 2100 (Practice Test #3)

A marketing firm is studying consumer preferences for winter fashions in four different months. From a population of women 18 to 21 years of age, a random sample of 100 women was selected in January. Another random sample of 100 women was selected in March. Another random sample of 100 women was selected in June. Another random sample of 100 women was selected in September. What is the sample size?

100

What is the interpretation of a 96% confidence level?

Approximately 96 out of 100 such intervals would include the true value of the population parameter.

How is the t-distribution similar to the standard z-distribution?

Both are continuous distributions.

A statewide sample survey is to be conducted. First, the state is subdivided into counties. Seven counties are selected at random, and further sampling is concentrated on these seven counties. What type of sampling is this?

Cluster sampling

What kind of distribution is the t-distribution?

Continuous

What statement do we make that determines if the null hypothesis is rejected?

Decision rule

A Type II error is the probability of rejecting the null hypothesis when it is actually true.

FALSE

A point estimate is a range of values used to estimate a population parameter.

FALSE

A point estimate is a single value used to estimate a population parameter.

FALSE

A z-statistic is used for a problem involving any sample size and an unknown population standard deviation.

FALSE

Based on 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.

FALSE

The standard error of the mean is also called the sampling error.

FALSE

When deciding to collect sample information rather than collecting information from the population, the amount of time required to collect the information is unimportant.

FALSE

What is a Type II error?

Failing to reject a false null hypothesis

Define the level of significance.

It is the probability of a Type I error.

Of the following characteristics, the t-distribution and z-distribution are the same in all but one. Which one is it?

Mean = 0, and standard deviation = 1

What is the difference between a sample mean and the population mean called?

Sampling error

Which of the following is not one of the six steps in the hypothesis testing procedure?

Select a level for β.

Manufacturers were subdivided into groups by volume of sales. Those with more than $100 million in sales were classified as large; those from $50 to $100 million as medium size; and those between $25 and $50 million, and so on. Samples were then selected from each of these groups. What is this type of sampling called?

Stratified random sampling

When dividing a population into subgroups so that a random sample from each subgroup can be collected, what type of sampling is used?

Stratified random sampling

Suppose we select every fifth invoice in a file. What type of sampling is this?

Systematic

A test statistic is a value computed from sample information that is used to test the null hypothesis.

TRUE

An example of a hypothesis is: A person is innocent until proven guilty.

TRUE

Assuming that the null hypothesis is true, a p-value is the probability of observing a sample value as extreme as, or more extreme than, the observed sample observation.

TRUE

For the sampling distribution of sample means, standard error will decrease as sample size increases.

TRUE

Hypothesis testing is a procedure that uses sample evidence and probability theory to decide whether to reject or fail to reject a hypothesis.

TRUE

It is often not feasible to study the entire population because it is impossible to observe all the items in the population.

TRUE

The 95% confidence interval states that 95% 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 Greek letter used to represent the probability of a Type I error is alpha (α).

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, even when the population is skewed or uniform.

TRUE

The level of significance is the probability of rejecting the null hypothesis when it is actually true.

TRUE

The probability of a Type II error is represented by the Greek symbol β.

TRUE

The standard error of the mean measures the dispersion of the sampling distribution of the sample mean.

TRUE

To determine the size of a sample, the standard deviation of the population must be estimated by either taking a pilot survey or by approximating it based on knowledge of the population.

TRUE

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

TRUE

When using the t-distribution to calculate a confidence interval, we assume that the population of interest is normal or nearly normal.

TRUE

Which statement(s) is(are) correct about the t-distribution?

The mean is zero. Its shape is symmetric. Its dispersion is based on degrees of freedom. *All apply.*

In hypothesis testing, what is the level of significance?

The risk of rejecting the null hypothesis when it is true. A value symbolized by the Greek letter α. A value between 0 and 1. It is selected before a decision rule can be formulated. *All of the answers apply.*

When testing the safety of cars using crash tests, a sample of one or two cars is used because ___________.

cars are destroyed

To study the population of consumer perceptions of new technology, sampling of the population is preferred over surveying the population because _________.

it is quicker

When all the items in a population have an equal chance of being selected for a sample, the process is called _________________.

simple random sampling

Which of the following is the standard error of the mean?

σ/√n