Test Bank

Chapter 9: Hypothesis Testing: A Conceptual Introduction

Multiple Choice

1. In hypothesis testing, the symbol H_o is used to denote ______.

A. the alternative hypothesis

B. the null hypothesis

C. the χ² statistic

D. the level of measurement

2. In hypothesis testing, the symbol H₁ is used to denote ______.

A. the alternative hypothesis

B. the null hypothesis

C. the chi-square statistic

D. the level of measurement

3. The hypothesis predicting that there is a relationship between the independent and dependent variables is known as ______ in scientific research.

A. the null hypothesis

B. the variance statement

C. the alternative hypothesis

D. the inferential hypothesis

4. A null hypothesis is ______.

A. a statement regarding the probability that the level of measurement of the independent variable of interest is appropriate for the desired inferential analysis

B. a statement predicting that any relationship existing between two or more variables of interest is due to the significance of the χ² statistic

C. a statement predicting that there is a relationship between the independent and dependent variables

D. a statement predicting that there is no relationship between the independent and dependent variables

5. In scientific research, the default assumption regarding the null and alternative hypotheses is ______.

A. that there is a relationship between the independent variable and dependent variables

B. that the alternative hypothesis reflects an accurate state of affairs for the two variables under investigation

C. that there is no relationship between the independent and dependent variables

D. that the alternative hypothesis should be accepted prior to the start of any statistical analysis to help alleviate any concerns pertaining to reliability and validity

6. The ultimate goal in conducting a statistical test is ______.

A. to decide whether to retain the null hypothesis or to reject the null hypothesis

B. to decide whether to accept the alternative hypothesis or reject the alternative hypothesis

C. to decide whether to reject the null hypothesis or accept the alternative hypothesis

D. to decide whether to retain the alternative hypothesis or to retain the null hypothesis

7. If a researcher rejects the H_o when it is in fact true, what type of error has been made?

A. a Type I

B. a Type II

C. No error has been made, this was a correct decision.

D. a Type III

8. What assumption does a researcher make from the outset of a hypothesis-testing procedure?

A. the researcher assumes that the alternative hypothesis is true.

B. the researcher makes absolutely no assumptions, instead allowing the data to determine if it is the H_o or the H₁ that is correct.

C. the researcher assumes both the H_o and the H₁ are correct.

D. the researcher assumes that the H_o is correct.

9. If the H_o is true and a researcher retains it, which of the following scenarios has occurred?

A. The researcher has committed a Type I error.

B. The researcher has committed a Type II error.

C. The researcher has committed an ecological fallacy.

D. The researcher has committed no error.

10. Which of the following is true with respect to researchers and the possibility of errors?

A. Researchers can minimize the probability that they are wrong about a decision, but they can never eliminate it.

B. Researchers can eliminate error by establishing the confidence level at a higher rate.

C. Researchers can eliminate error by manipulating the standard error through careful analytic technique.

D. Researchers can prevent error from entering into a study by controlling the collection of data and preventing standard error from tainting the data during analysis.

11. Bivariate analysis involves ______.

A. two separate statistical operations to help minimize standard error

B. a descriptive analysis followed by an inferential analysis

C. the analysis of two variables

D. the creation of two α levels to help minimize any error and prevent the possibility of making a Type II error

12. A professor studying homicides across racial groups has an independent variable defined as race, with labels of White, Black, Latino, Native American, and Asian. She has a dependent variable labeled homicide, which is a whether or not a homicide has occurred during each month of the calendar year. Based on the levels of measurement of the independent variable and dependent variable, what type of analysis would the professor use to test for a relationship between the two variables?

A. With a continuous independent variable and a categorical dependent variable, the best course would be an ANOVA or t test.

B. With a continuous independent variable and a categorical dependent variable, the wisest move would be a χ² or correlation.

C. With a categorical independent variable and a continuous dependent variable, the best choice would be to run a t test.

D. With a categorical independent variable and a categorical dependent variable, the best decision would be to run a χ².

13. A researcher is studying the relationship between the age at which a person begins committing delinquent or criminal offenses and the number of offenses that person commits during her or his life. The independent variable is age (measured in years), and the dependent variable is offenses (measured as the total number of lifetime offenses). Based on the variables’ levels of measurement, what hypothesis-testing procedure is appropriate?

A. With a categorical independent variable and a continuous dependent variable, ANOVA is correct.

B. With a continuous independent variable and a continuous dependent variable, correlation is correct.

C. With a categorical independent variable and a continuous dependent variable, correlation is correct.

D. With a categorical independent variable and categorical dependent variable, a t test is correct.

14. During hypothesis testing, ______.

A. it is useful to use a five-step sequence in order to lend structure to the procedure

B. it is useful to proceed by what “feels right,” as statistical analysis is often as much art as science

C. it is not practical to develop too much of a framework or outline as that constricts creativity during the analytical phase of a study

D. it is useful for a researcher to select an analytic test with which he or she is more comfortable, as this is an excellent way to help minimize error

15. In those instances in which a sample statistic is not equal to a population parameter, there are two potential explanations for the mismatch. Which of the following is one potential reason for such a discrepancy?

A. Observed differences are due to a third variable, heretofore gone unnoticed by the researcher.

B. Observed differences are due to the adverse effects of standard error.

C. Any observed disparity might be due to a confounding.

D. Any observed disparity may be a meaningless fluke.

16. In those instances in which a sample statistic is not equal to a population parameter, there are two potential explanations for the mismatch. Which of the following is one potential reason for such a discrepancy?

A. The disparity is caused by the erroneous use of the z distribution when t should have been used instead.

B. Observed differences are the product of the omitted variable bias.

C. The disparity may indicate a genuine, bona fide difference between the statistic and the parameter.

D. Any of the above is a possible explanation for an observed difference of this sort.

17. Which of the following is the key to deciding the type of statistical analysis that is correct to use for a hypothesis test??

A. the amount of data to be analyzed

B. the researcher’s needs and desires

C. the variables’ level of measurement

D. sample size: N

18. If a researcher wishes to be able to reject the H_o, what must occur?

A. The critical value must not exceed the obtained value of the test statistic.

B. The critical value must exceed the obtained value of the test statistic.

C. The observed value of the test statistic must be equal to the critical value.

D. The observed value of the test statistic and the critical value must be equal to the α level.

19. What is meant by the term inferential analysis?

A. It is the process of generating the null and alternative hypotheses.

B. It is the process of generalizing from a population parameter to a sample statistic.

C. It is the process of generalizing from a sample to a population; the use of a sample statistic to estimate a population parameter.

D. It is the statistical process through which a researcher attempts to diminish error that can creep into a study.

20. A ______ occurs when a false null is inaccurately retained.

A. Type I error

B. false hypothesis test

C. Type II error

D. variable test

21. The hypothesis-testing procedure used when an independent variable is categorical with three or more classes and a dependent variable is continuous is ______.

A. t test

B. bivariate regression

C. χ²

D. ANOVA

22. What are those results that are actually seen?

A. empirical outcomes

B. observed outcomes

C. both A and B

D. neither A nor B

23. What are the results you anticipate seeing on the basis of probability theory?

A. expected outcomes

B. predicted outcomes

C. both A and B

D. neither A nor B

24. Which kind of analytical test is used when the dependent variable is continuous and the independent variable is categorical with three or more classes?

A. χ²

B. bivariate regression

C. t test

D. ANOVA

25. What is the first step of hypothesis testing?

A. identify the distribution and compute the degrees of freedom

B. compute the obtained value of the test statistic

C. identify the critical value of the test statistic, and state the decision rule

D. state the null (H₀) and alternative (H₁) hypotheses

26. A ______ error occurs when a true null hypothesis is erroneously rejected.

A. type I

B. type II

C. type III

D. none of these

27. To account for ______ inferential statistics utilize sampling distributions to make probabilistic prediction about sample statistics.

A. rounding error

B. sampling error

C. population error

D. none of these

28. The proper test to use in any particular hypothesis-testing scenario is determined by the ______ of the variables you are using.

A. level of measurement

B. sampling distribution

C. population error

D. none of these

29. Which of the following terms refers to variation that is like the white noise in the background when it comes to sampling.

A. type I error

B. type II error

C. sampling error

D. none of these

30. “Crime rates will vary by gender” is what kind of hypothesis?

A. null hypothesis

B. nondirectional hypothesis

C. directional hypothesis

D. none of these

31. “Men are more likely to have a greater number of arrests than women” is what kind of hypothesis?

A. null hypothesis

B. nondirectional hypothesis

C. directional hypothesis

D. none of these

32. “Crime rates do not vary by gender” is what kind of hypothesis?

A. null hypothesis

B. nondirectional hypothesis

C. directional hypothesis

D. none of these

33. Wrongfully convicting an innocent defendant is what kind of error?

A. sampling error

B. type I error

C. type II error

D. none of these

34. Approving an ineffective drug for the market is what kind of error?

A. sampling error

B. type I error

C. type II error

D. none of these

35. Incorrectly acquitting a guilty defendant is what kind of error?

A. sampling error

B. type I error

C. type II error

D. none of these

1. Hypothesis testing involves the use of a sample as a means of drawing a conclusion about a population of interest.

2. The proper test to use in a given hypothesis-testing situation is determined by the level of measurement of the variables being examined.

3. The ultimate goal for the quantitative researcher is to be able to generalize from a population to a sample.

4. The probability of empirical outcomes is the basis of inferential statistics.

5. The alternative hypothesis is essentially the opposite of the null hypothesis.

6. The general goal in conducting a statistical test is to decide whether to retain the null hypothesis or to reject the null hypothesis.

7. According to your text, correlation can be used with either categorical or continuous data.

8. The χ² statistical test is an operation designed to be used with categorical data.

9. If a scientist inadvertently selected the wrong statistical test for the level of measurement for his or her data, the end result would still yield a correct outcome as the SPSS software is powerful enough to detect and fix simple mistakes.

10. The SPSS program is a great tool for the novice researcher due to the fact that it always provides error messages to assist in detecting mistakes.

11. The obtained value calculated during the analytical portion of an analysis must exceed the critical value in order for the null to be rejected.

12. Once a researcher has completed the analytical portion of an analysis, there is little need to fret over the interpretation of results and determination of substantive conclusions as an editorial body comprised of peers and other experts always help determine whether the results are accurate and meaningful.

13. In hypothesis testing, researchers make use of a probability distribution to find out whether a sample statistic has a low or high probability of occurrence.

14. In hypothesis testing, the key distinction is that between categorical and continuous variables.

15. Expected outcomes and observed outcomes are the results you anticipate seeing on the basis of probability theory.

16. The process of generalizing from a sample to a population through the use of a sample statistic in an effort to estimate a population parameter is known as hypothesis testing.

17. Expected outcomes are the results you anticipate seeing on the basis of probability theory.

18. In an inferential test, the statement predicting that there is no relationship between the independent and dependent variable is referred to as the alternative hypothesis.

19. In inferential statistics, the symbol used to denote a null hypothesis is H_o.

20. In inferential statistics, the symbol used to denote an alternative hypothesis is H₁.

1. Briefly explain the difference between a Type I and Type II error.

2. Discuss what an ANOVA test is.

3. A researcher is investigating differences in homicide rates across northern and southern cities. She collects data and finds that the mean homicide rate in four large southern cities is 95.45.The mean homicide rate for four large northern cities was 81.09. What would this researcher’s null and alternative hypotheses look like? Write your answers out in words.

4. Now, use the null and alternative hypotheses that you constructed in the last question and rewrite them using symbols instead of words.

5. There has long been an analogy between hypothesis testing and court proceedings. Explain how the presumption of innocence during a trial could possibly be related to hypothesis testing in statistics.