Question 1

Hypotheses are stated in two basic forms: __________ & _____________.
A)Null and Fake
B)Null and Real
C)Null and Alternative
D)Alternative and Real

Accepted Answer

Hypotheses are stated in the form of null and alternative hypotheses. The null hypothesis represents the default or status quo position, while the alternative hypothesis represents the researcher's proposed explanation or prediction.

Question 2

The z-test would be appropriate for testing three or more proportions when the sample size is less than 30.

Accepted Answer

The z-test assumes that the sample size is large enough (typically greater than 30) for the Central Limit Theorem to apply. For small sample sizes (less than 30), the appropriate test to use is typically the t-test.

Question 3

If a particular difference is large enough to be unlikely to have occurred because of chance or sampling error,then the difference is statistically significant.

Accepted Answer

This is the definition of statistical significance. A large enough difference that cannot be explained by chance or sampling error is considered statistically significant.

Question 4

In marketing research,the basic motive for making statistical inferences is to generalize from sample results to population characteristics.

Accepted Answer

The purpose of making statistical inferences is to draw conclusions about a population based on a sample. This requires generalizing from the sample to the population, and therefore the statement is true.

Question 5

The number of observations minus the number of assumptions necessary to calculate a statistic equals:
A)the Z score.
B)ANOVA.
C)random variation.
D)degrees of freedom.

Accepted Answer

The difference between the number of observations and the number of assumptions necessary to calculate a statistic is known as degrees of freedom. Therefore, the correct option is D.

Question 6

A test to determine whether the difference between proportions is greater than would be expected because of sampling error is which of the following?
A)hypothesis test of proportions
B)t-test
C)z-test
D)chi-square test
E)none of these

Accepted Answer

A hypothesis test of proportions is used to compare two proportions and determine if their difference is statistically significant or simply due to chance. It is the appropriate test for determining if the difference between two proportions is greater than would be expected because of sampling error. The t-test, z-test, and chi-square test are used for different types of statistical analysis and are not appropriate for this situation.

Question 7

A researcher is attempting to determine which ethnic group is more likely to go to the movies at a movie theatre.The dependent variable is metric.Which of the following tests is most appropriate?
A)analysis of variance
B)t-test
C)z-test
D)chi-square test
E)none of these

Accepted Answer

Analysis of variance (ANOVA) is used when comparing the means of more than two groups. In this case, the independent variable is ethnicity (which has more than two categories), and the dependent variable is the frequency of going to the movies. Therefore, ANOVA is the most appropriate choice. T-tests and z-tests are used for comparing means between two groups, and chi-square tests are used for analyzing categorical data.

Question 8

This particular test involves evaluating the differences in observed and expected frequencies in a crosstab matrix.
A)hypothesis test of proportions
B)t-test
C)z-test
D)chi-square test
E)none of these

Accepted Answer

The chi-square test is used to evaluate whether or not there is a significant difference between observed and expected frequencies in a categorical data set, as represented in a crosstab matrix. It is often used in social science research to analyze survey or experimental data.

Question 9

An assumption or theory that a researcher or manager makes about some characteristic of the population under study is an inference.

Accepted Answer

An assumption or theory that a researcher or manager makes about some characteristic of the population under study is a hypothesis, not an inference. An inference is a conclusion reached on the basis of evidence and reasoning.

Question 10

A(n)____ test is a test of the probability that a particular calculated value could have been due to chance.
A)Q
B)Z
C)T
D)F

Accepted Answer

The answer of A(n)____ test is a test of the...

Question 11

In related samples,the measurement of the variable of interest has no influence on the measurement of the variable in another sample.

Accepted Answer

In related samples, the measurements of the variable of interest in one sample are often related or paired with measurements in another sample, influencing the analysis and interpretation of the relationship between the samples.

Question 12

The last step in testing a hypothesis is the development of a decision rule.

Accepted Answer

The last step in testing a hypothesis typically involves making a decision on the hypothesis based on the results of the test, not the development of a decision rule. The development of a decision rule is one of the earlier steps, where criteria for rejecting or failing to reject the hypothesis are established.

Question 13

A(n)________________ is a standard used to determine whether to reject or fail to reject the null hypothesis.
A)Decision rule
B)Common rule
C)Determined rule
D)Assessment rule

Accepted Answer

The decision rule is a standard used in hypothesis testing to decide whether to reject or fail to reject the null hypothesis. It is based on the significance level, which is predetermined by the researcher or set to a standard value, usually 5% or 1%. The decision rule specifies the critical values or the rejection regions for the test statistic and is used to make a decision on whether the observed data provides enough evidence to reject the null hypothesis and support the alternative hypothesis.

Question 14

When testing hypotheses about frequency distributions,nominal variables are acceptable.

Accepted Answer

Nominal variables refer to categorical data, which can be tested and analyzed through frequency distributions. Therefore, hypotheses about frequency distributions can be tested with nominal variables.

Question 15

What determines the decision of whether to use a one-tailed test or a two-tailed test when testing hypotheses to make inferences about a population mean?
A)the sample size and the estimated standard error
B)the nature of the situation and what the researcher is trying to demonstrate
C)the level of significance of the test
D)the sample size relative to the population size
E)the standard error relative to the sample variance

Accepted Answer

The decision to use a one-tailed test or a two-tailed test depends on the nature of the situation and what the researcher is trying to demonstrate. A one-tailed test is used when the researcher is interested in either a specific direction of difference or knows in advance the direction of the difference. For example, if the researcher is testing a hypothesis that a new treatment will be more effective than an existing treatment, a one-tailed test would be appropriate. On the other hand, a two-tailed test is used when the researcher is interested in detecting any difference from the null hypothesis, regardless of the direction. For example, if the researcher is investigating whether there is a difference in the mean weight of apples between two farms, a two-tailed test would be appropriate. The level of significance also plays a role in the decision, but it is not the determining factor.

Question 16

Researchers must be careful to distinguish statistical significance from:
A)mathematical significance.
B)chance significance.
C)practical significance.
D)random significance.

Accepted Answer

Statistical significance refers to the probability that the observed results are not due to chance. However, even if a result is statistically significant, it may not be practically significant or meaningful in the real world. Therefore, researchers must always consider practical significance in addition to statistical significance. Mathematical significance and random significance are not commonly used terms in research, and chance significance may be confused with statistical significance.

Question 17

Mathematical differences are the same as statistically significant differences.

Accepted Answer

Mathematical differences refer to absolute differences between values or measurements, whereas statistically significant differences refer to the amount of variability in the data and the likelihood that any observed difference is not due to chance. Just because there is a mathematical difference between two groups does not necessarily mean that the difference is statistically significant.

Question 18

Hypotheses about frequency distributions that involve one or more nominally scaled variables can be tested using ____________.
A)chi-square test
B)t-test
C)f-test
D)z-test
E)ANOVA test

Accepted Answer

The chi-square test is used to analyze the difference between observed and expected frequencies in a nominal distribution. It is the most appropriate test for hypotheses that involve one or more nominally scaled variables. The t-test and f-test are used for hypotheses involving interval or ratio scale variables, while the z-test is used to test hypotheses about population means when the population standard deviation is known. ANOVA is used for testing hypotheses involving one independent variable and one dependent variable with interval or ratio scales.

Question 19

Type II error is most closely related to which of the following?
A)beta
B)alpha
C)omega
D)all of these
E)none of these

Accepted Answer

Type II error is also known as a false negative, where the null hypothesis is not rejected when it is actually false. Beta is the probability of committing a Type II error, so option A is the closest and most appropriate answer. Alpha is related to Type I error, which is the rejection of the null hypothesis when it is actually true. Omega is not a commonly used term in hypothesis testing. Therefore, D) all of these, and E) none of these are not the best choices.

Question 20

In testing a hypothesis from a random sample involving three or more means,the appropriate test would be a one-way ANOVA.

Accepted Answer

One-way ANOVA is the appropriate test to compare three or more means from a random sample.

Quiz 16: Statistical Testing of Differences and Relationships

Hypotheses are stated in two basic forms: & ___.

The z-test would be appropriate for testing three or more proportions when the sample size is less than 30.

If a particular difference is large enough to be unlikely to have occurred because of chance or sampling error,then the difference is statistically significant.

In marketing research,the basic motive for making statistical inferences is to generalize from sample results to population characteristics.

The number of observations minus the number of assumptions necessary to calculate a statistic equals:

A test to determine whether the difference between proportions is greater than would be expected because of sampling error is which of the following?

A researcher is attempting to determine which ethnic group is more likely to go to the movies at a movie theatre.The dependent variable is metric.Which of the following tests is most appropriate?

This particular test involves evaluating the differences in observed and expected frequencies in a crosstab matrix.

An assumption or theory that a researcher or manager makes about some characteristic of the population under study is an inference.

A(n) ____ test is a test of the probability that a particular calculated value could have been due to chance.

In related samples,the measurement of the variable of interest has no influence on the measurement of the variable in another sample.

The last step in testing a hypothesis is the development of a decision rule.

A(n) ________________ is a standard used to determine whether to reject or fail to reject the null hypothesis.

When testing hypotheses about frequency distributions,nominal variables are acceptable.

What determines the decision of whether to use a one-tailed test or a two-tailed test when testing hypotheses to make inferences about a population mean?

Researchers must be careful to distinguish statistical significance from:

Mathematical differences are the same as statistically significant differences.

Hypotheses about frequency distributions that involve one or more nominally scaled variables can be tested using ____________.

Type II error is most closely related to which of the following?

In testing a hypothesis from a random sample involving three or more means,the appropriate test would be a one-way ANOVA.