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Unit 9: Hypothesis Testing - Practice Quiz

DEMGN832 — Research Methodology 60 Questions
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1 What is a hypothesis in research?

Hypothesis definition Easy
A. A list of collected research data
B. A summary of published research
C. A testable statement about a population
D. A confirmed law about a population

2 Which characteristic should a useful research hypothesis have?

Hypothesis definition Easy
A. It should always predict no difference
B. It should be based only on opinion
C. It should contain several unrelated claims
D. It should be testable with evidence

3 What is the main purpose of hypothesis testing?

Hypothesis testing process Easy
A. To describe data without making a decision
B. To prove that every sample is accurate
C. To remove all variation from the data
D. To use sample data to evaluate a claim

4 What does the significance level represent?

Hypothesis testing process Easy
A. The probability of a Type II error
B. The size of the population
C. The value of the sample mean
D. The probability of a Type I error

5 When is the null hypothesis usually rejected using the p-value method?

Hypothesis testing process Easy
A. When the p-value is greater than the test statistic
B. When the p-value is less than
C. When the p-value is greater than
D. When the p-value is equal to the sample size

6 Which symbol commonly represents the null hypothesis?

Types of hypotheses Easy
A.
B.
C.
D.

7 Which hypothesis usually states that there is no difference or effect?

Types of hypotheses Easy
A. Research hypothesis
B. Null hypothesis
C. Alternative hypothesis
D. Directional hypothesis

8 Which alternative hypothesis describes a two-tailed test for a population mean?

Types of hypotheses Easy
A.
B.
C.
D.

9 When is a one-sample t-test commonly used?

Hypothesis testing procedure for t-tests Easy
A. When no sample data are available
B. When the outcome is purely categorical
C. When the population standard deviation is unknown
D. When the population standard deviation is known

10 What degrees of freedom are used in a one-sample t-test with sample size ?

Hypothesis testing procedure for t-tests Easy
A.
B.
C.
D.

11 Which distribution is used to find critical values for a t-test?

Hypothesis testing procedure for t-tests Easy
A. Poisson distribution
B. Standard normal distribution
C. Uniform distribution
D. Student's t-distribution

12 When is a one-sample z-test for a mean generally appropriate?

Hypothesis testing procedure for z-tests Easy
A. When observations are deliberately paired
B. When the population standard deviation is known
C. When the population standard deviation is unknown
D. When the data contain only category names

13 Which distribution provides critical values for a z-test?

Hypothesis testing procedure for z-tests Easy
A. Standard normal distribution
B. Chi-square distribution
C. Student's t-distribution
D. Binomial distribution

14 For a two-tailed z-test at , which critical values are commonly used?

Hypothesis testing procedure for z-tests Easy
A. and
B. and
C. and
D. and

15 A one-sample test for a mean compares the sample mean with what value?

Differences for a single population Easy
A. A second independent sample mean
B. A hypothesized population mean
C. A paired-sample difference mean
D. A calculated population range

16 Which null hypothesis is suitable for testing whether a population mean equals ?

Differences for a single population Easy
A.
B.
C.
D.

17 What does an independent two-sample test compare?

Differences for two populations Easy
A. The means of two separate groups
B. Two variables from the same individual
C. A sample mean and a known variance
D. The means of one group at two times

18 Which null hypothesis represents no difference between two population means?

Differences for two populations Easy
A.
B.
C.
D.

19 Which situation is most suitable for a paired-samples test?

Differences for paired samples Easy
A. Blood pressure measured before and after treatment
B. Test scores from two different schools
C. Heights measured in two independent classes
D. Blood pressure measured in two unrelated cities

20 In a paired t-test, what values are directly analyzed?

Differences for paired samples Easy
A. Frequencies within each response category
B. Differences within each matched pair
C. Ratios between two population sizes
D. Totals within each independent group

21 Which statement is the best example of a statistical hypothesis?

Hypothesis definition Medium
A. The observed waiting time seems reasonably short
B. The waiting area should have additional seating
C. Customers generally dislike waiting for service
D. The population mean waiting time is less than 15 minutes

22 A researcher predicts that a training program increases the average productivity score above 80. Which statement represents the research hypothesis?

Hypothesis definition Medium
A.
B.
C.
D.

23 A hypothesis test produces a p-value of at a significance level of . What is the appropriate decision?

Hypothesis testing process Medium
A. Retain because the p-value is above
B. Increase because the result is inconclusive
C. Reject because the p-value is below
D. Reject because the p-value is below

24 A researcher rejects a true null hypothesis. Which error has occurred?

Hypothesis testing process Medium
A. A Type II error
B. A sampling-frame error
C. A Type I error
D. A measurement error

25 A company claims that the mean battery life is different from 10 hours. Which pair of hypotheses is appropriate?

Types of hypotheses Medium
A. and
B. and
C. and
D. and

26 Which alternative hypothesis requires a left-tailed test?

Types of hypotheses Medium
A.
B.
C.
D.

27 A sample of 25 observations has and . To test , what is the one-sample t-statistic?

Hypothesis testing procedure for t-tests Medium
A.
B.
C.
D.

28 For a right-tailed t-test with and , the critical value is . If the calculated statistic is , what should the researcher conclude?

Hypothesis testing procedure for t-tests Medium
A. Reject because
B. Retain because
C. Retain because
D. Reject because

29 Two independent samples have , , , , and . Using , what is the test statistic?

Hypothesis testing procedure for t-tests Medium
A.
B.
C.
D.

30 A population has known standard deviation . For a sample with and , what is the z-statistic for testing ?

Hypothesis testing procedure for z-tests Medium
A.
B.
C.
D.

31 In a sample of 400 customers, 216 prefer a new product, so . What is the z-statistic for testing ?

Hypothesis testing procedure for z-tests Medium
A.
B.
C.
D.

32 A two-tailed z-test uses . If the calculated statistic is , what is the correct decision?

Hypothesis testing procedure for z-tests Medium
A. Reject because
B. Retain because
C. Reject because
D. Retain because

33 A university tests whether the mean study time differs from 12 hours per week. A sample gives a 95% confidence interval of . What conclusion matches a two-tailed test at ?

Differences for a single population Medium
A. Retain because 12 is outside the interval
B. Retain because the interval is sufficiently narrow
C. Reject because 12 is outside the interval
D. Reject because 12 is below the sample mean

34 A researcher tests against and obtains . At , the right-tail critical value is . What is the conclusion?

Differences for a single population Medium
A. Retain and conclude that the proportion exceeds 0.40
B. Reject and conclude that the proportion is below 0.40
C. Reject and conclude that the proportion exceeds 0.40
D. Retain and conclude that the proportion equals 0.40

35 Two independent populations have known standard deviations. Sample results are , , , , , and . What is the z-statistic for testing ?

Differences for two populations Medium
A.
B.
C.
D.

36 When testing with two independent samples, which estimate is normally used to calculate the null standard error?

Differences for two populations Medium
A. The second sample proportion
B. The first sample proportion
C. The pooled sample proportion
D. The difference in sample proportions

37 A test comparing two independent means gives a p-value of . At , which interpretation is appropriate?

Differences for two populations Medium
A. There is sufficient evidence that the means are exactly equal
B. There is sufficient evidence of a difference between the means
C. There is insufficient evidence of a difference between the means
D. There is insufficient evidence that either population has a mean

38 A paired-samples study has 16 pairs, a mean difference of , and a standard deviation of differences of . What is the paired t-statistic for testing ?

Differences for paired samples Medium
A.
B.
C.
D.

39 Which study design is most appropriate for a paired-samples hypothesis test?

Differences for paired samples Medium
A. Measuring the same employees before and after training
B. Comparing employees from two unrelated organizations
C. Measuring one variable in a single random sample
D. Comparing two independently selected customer groups

40 Why can a paired-samples test be more powerful than an independent-samples test for matched observations?

Differences for paired samples Medium
A. It avoids estimating the variability of the differences
B. It always increases the number of measured individuals
C. It removes some variation between matched individuals
D. It eliminates all sampling error from the observations

41 A researcher predicts that a training program increases the mean reaction speed above a known population mean of ms. Which formulation best represents the hypotheses for a one-tailed test?

Hypothesis definition Hard
A. ,
B. ,
C. ,
D. ,

42 A study obtains after testing against . Which conclusion is logically justified at and ?

Hypothesis testing process Hard
A. Reject at both significance levels
B. Reject at but not at
C. Reject at but not at
D. Fail to reject at both significance levels

43 A statistically significant result is obtained from a very large sample, but the estimated mean difference is practically negligible. Which interpretation is most defensible?

Hypothesis testing process Hard
A. The result proves that the sample estimate is unbiased
B. The result is statistically detectable but may lack practical importance
C. The null hypothesis must be substantively false
D. The test is invalid because significance requires a large effect

44 A researcher states that a treatment changes mean blood pressure but does not specify the direction of change. Which hypothesis structure is appropriate?

Types of hypotheses Hard
A. ,
B. ,
C. ,
D. ,

45 Which statement correctly distinguishes a simple hypothesis from a composite hypothesis?

Types of hypotheses Hard
A. A simple hypothesis uses a sample statistic; a composite hypothesis uses a population parameter
B. A simple hypothesis is always directional; a composite hypothesis is always nondirectional
C. A simple hypothesis is tested with ; a composite hypothesis is tested with
D. A simple hypothesis specifies one parameter value; a composite hypothesis specifies a set of values

46 A study compares two population means using and . What type of alternative and rejection region does this imply?

Types of hypotheses Hard
A. Nondirectional alternative with rejection near zero
B. Two-tailed alternative with rejection in both tails
C. Right-tailed alternative with rejection in the upper tail
D. Left-tailed alternative with rejection in the lower tail

47 A sample of observations has , , and the hypothesized mean is . For a two-tailed test at , what is the correct decision using a one-sample -test?

Hypothesis testing procedure for t-tests Hard
A. Fail to reject because is below
B. Reject because exceeds
C. Fail to reject because is below
D. Reject because exceeds

48 A one-sample -test is used with . If the alternative is and , which critical-value rule is correct?

Hypothesis testing procedure for t-tests Hard
A. Reject when using degrees of freedom
B. Reject when using degrees of freedom
C. Reject when using degrees of freedom
D. Reject when using degrees of freedom

49 Which condition most directly justifies using a one-sample -test instead of a one-sample -test for a mean?

Hypothesis testing procedure for t-tests Hard
A. The population standard deviation is known and the sample is small
B. The sample mean is equal to the hypothesized population mean
C. The population standard deviation is unknown and is estimated by the sample standard deviation
D. The alternative hypothesis is directional rather than nondirectional

50 A known population standard deviation is . For , , and versus , what is the statistic and decision at ?

Hypothesis testing procedure for z-tests Hard
A. ; fail to reject
B. ; reject
C. ; fail to reject
D. ; reject

51 For a two-tailed -test at significance level , which rejection rule is correct?

Hypothesis testing procedure for z-tests Hard
A. Reject when
B. Reject when
C. Reject when
D. Reject when

52 A researcher uses a -test for a population mean because , but the population standard deviation is unknown and the population distribution is strongly skewed. Which criticism is strongest?

Hypothesis testing procedure for z-tests Hard
A. The sample must contain exactly two observations per parameter
B. A large sample never permits a normal approximation
C. The test should account for estimating , although large may make and similar
D. The -test is automatically invalid whenever skewness exists

53 A population has known . A sample of yields . Testing against at , what conclusion follows?

Differences for a single population Hard
A. Reject because exceeds
B. Fail to reject because is below
C. Fail to reject because is below
D. Reject because exceeds

54 A test of against produces with . If the one-tailed critical value at is , what is the correct conclusion?

Differences for a single population Hard
A. Fail to reject because the statistic is negative
B. Reject and conclude the mean is below
C. Reject and conclude the mean equals
D. Fail to reject because is below

55 Two independent groups have , , , , and sample sizes , . Which test statistic is appropriate when equal population variances are not assumed?

Differences for two populations Hard
A.
B.
C.
D.

56 Two independent samples are compared with . A 95% confidence interval for is . What is the corresponding hypothesis-test conclusion at ?

Differences for two populations Hard
A. Fail to reject because zero lies inside the interval
B. Reject because the interval is centered above zero
C. Fail to reject because the interval contains no negative values
D. Reject because the interval contains positive values

57 Two independent population means are compared. Group 1 has and group 2 has . Under the equal-variance assumption, what degrees of freedom are used for the pooled two-sample -test?

Differences for two populations Hard
A.
B.
C.
D.

58 In a before-after study, the differences are defined as . Testing whether the treatment increases the outcome requires which alternative hypothesis?

Differences for paired samples Hard
A.
B.
C.
D.

59 For matched pairs, the mean difference is and the standard deviation of differences is . Testing against a two-sided alternative, what is the test statistic?

Differences for paired samples Hard
A. with
B. with
C. with
D. with

60 Why can a paired-samples test have greater power than an independent-samples test using the same participants in each condition?

Differences for paired samples Hard
A. Pairing guarantees that every treatment effect is statistically significant
B. Pairing can remove between-subject variability from the difference scores
C. Pairing automatically increases the number of independent observations
D. Pairing removes the need to estimate a standard deviation
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