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A teacher is experimenting with a new computer-based instruction and conducts a study to test its effectiveness. In which situation could the teacher use a hypothesis test for matched pairs?

**A **The teacher gives each student in the class a pretest. Then she teaches a lesson using a computer program. Afterwards, she gives each student a post-test. The teacher wants to see if the difference in scores will show an improvement.

**B **The teacher randomly divides the class into two groups. One of the groups receives computer-based instruction. The other group receives traditional instruction without computers. After instruction, each student takes a test and the teacher wants to compare the performance of the two groups.

**C**The teacher uses a combination of traditional methods and computer-based instruction. She asks students which they liked better. She wants to determine if the majority prefer the computer-based instruction.

Question 2

Research suggests that identical twins have many similarities, such as body weights, even as adults. A sample of ten sets of identical twins were weighed and had their weights recorded in kilograms. The researcher wishes to test whether there is a statistically significant difference in adult weight between first-born and second-born identical twins.

Source: M. J. Tramo, W. C. Lodtus, T. A. Stukel, R. L. Green, J. B. Weaver, and M. S. Gazzaniga. “Brain Size, Head Size, and Intelligence Quotient in Monozygotic Twins.” *Neurology* 50, 1246–52.

Given the design of the study and the question of interest, which one of the following computer outputs is relevant to use?

**A **

**B **

**C**

**D **

Question 3

Some research suggests that first born children may have higher IQ scores than their later born siblings. Do first-born identical twins have higher IQ scores than their second-born sibling? Data from a 1998 study were analyzed to determine whether first-born identical twins have higher IQ scores than their second-born siblings. Ten pairs of adult identical twins were assessed and their Full Scale IQ scores were calculated.

Source: M. J. Tramo, W. C. Lodtus, T. A. Stukel, R. L. Green, J. B. Weaver, and M. S. Gazzaniga. “Brain Size, Head Size, and Intelligence Quotient in Monozygotic Twins.” *Neurology* 50, 1246–52.

Let μ1 and μ2 represent the mean Full Scale IQ score for *all *first-born identical twins and second-born identical twins, respectively, and let μd be the mean of the differences in IQ score

of all identical twins (IQ score of first-born twin - IQ score of second-born twin).

Which of the following are the appropriate null and alternative hypotheses?

**A **H0: μd = 0
Ha: μd > 0

**B **H0: μd = 0
Ha: μd < 0

**C**H0: μd > 0
Ha: μd = 0

**D **H0: μ1= μ2
Ha: μ1 > μ2

Question 4

Some research suggests that first born children may have higher IQ scores than their later born siblings. Do first-born identical twins have higher IQ scores than their second-born sibling? Data from a 1998 study were analyzed to determine whether first-born identical twins have higher IQ scores than their second-born siblings. Ten pairs of adult identical twins were assessed and their Full Scale IQ scores were calculated.

Source: M. J. Tramo, W. C. Lodtus, T. A. Stukel, R. L. Green, J. B. Weaver, and M. S. Gazzaniga. “Brain Size, Head Size, and Intelligence Quotient in Monozygotic Twins.” *Neurology* 50, 1246–52.

The following hypotheses were tested:

H0: μd = 0

Ha: μd > 0

The following is the (edited) output for the test:

Which of the following is an appropriate conclusion based on the output?

**A **The data provide sufficient evidence to reject H0and, thus, conclude that the mean Full Scale IQ score for first-born identical twins is higher than the mean Full Scale IQ score for second-born identical twins.

**B **The data provide sufficient evidence to reject H0. We therefore conclude the data do *not *provide evidence to conclude that the mean Full Scale IQ scores for first-born identical twins is higher than that of second-born identical twins.

**C**The data do not provide sufficient evidence to reject H0. We therefore conclude that the mean Full Scale IQ score for first-born identical twins is higher than the mean Full Scale IQ score for second-born identical twins.

**D **The data do not provide sufficient evidence to reject H0. In other words, based on the data we *cannot* conclude that the mean Full Scale IQ scores for first-born identical twins is higher than the mean Full Scale IQ score for second-born identical twins.

Question 5

In which of the following situations would it be appropriate to use a paired t-test to analyze the data? Check all that apply.

**A **A marriage therapist believes that many couples have different perspectives regarding the state of their marriages, prior to the start of couples therapy. In order to determine whether there is difference in marital satisfaction, prior to the start of couples therapy, each member of thirty married couples were individually given a marital satisfaction questionnaire. The mean marital satisfaction scores were then separately calculated for the group of husbands and the group of wives.

**B **A psychologist was interested in determining whether fraternal twins differ in terms the degree to which they are extroverts. A sample of 50 fraternal twins was given the Eysenck personality questionnaire to assess their levels of extraversion.

**C**A psychiatrist believes that a new medication (New Drug) is more effective at reducing the symptoms of depression than a placebo, sugar pill (Placebo). Sixty people with depression were randomly assigned to one of two groups: 1) New Drug or 2) Placebo and were given the assigned drug or sugar pill for 30 days. Each of the 60 participants then completed the Beck Depression Inventory and the mean depression score for the New Drug group is compared to the mean depression score for the Placebo group.

**D **A researcher is interested in determining the effects of sleep deprivation on the accuracy with which mazes are completed. Thirty people are given a test of mazes on Day 1 at 9 am and again on Day 2 at 9 pm after being kept awake for 36 hours. The researcher then compares the number of errors made on Day 1 to Day 2.

Question 6

Research suggests that the pressure of being timed may interfere with performance on tests that involve mathematical problems. A fictional study was conducted with 30 sixth graders. First, the sixth graders were given a math test that contained 50 problems and were told that they had only one hour to complete it (timed condition). The same sixth graders were later given a math test that contained 50 problems and were told that they could have as much time, as needed, to complete the test (unlimited time condition). The total number of correct answers for each sixth grader was then calculated for each condition. Then, for each student, the difference between the two scores (timed – untimed) was calculated. The researchers hypothesized that the sixth graders would get fewer correct answers when they took the test with a time limit than when they had unlimited time.

If μ1and μ2represent the number of correct answers during the timed condition and the unlimited time condition, respectively, and let μd be the mean of the differences in the number of correct answers (timed – untimed) of all sixth graders.

Which of the following are the appropriate null and alternative hypotheses?

**A **H0: μd = 0
Ha: μd > 0

**B **H0: μd = 0
Ha: μd < 0

**C**H0: μd < 0
Ha: μd = 0

**D **H0: μ1- μ2 = 0
Ha: μ1 - μ2 < 0

Question 7

Research suggests that the pressure of being timed may interfere with performance on tests that involve mathematical problems. A fictional study was conducted with 30 sixth graders. First, the sixth graders were given a math test that contained 50 problems and were told that they had only one hour to complete it (timed condition). The same sixth graders were later given a math test that contained 50 problems and were told that they could have as much time, as needed, to complete the test (unlimited time condition). The total number of correct answers for each sixth grader was then calculated for each condition. Then, for each student, the difference between the two scores (timed – untimed) was calculated. The researchers hypothesized that the sixth graders would get fewer correct answers when they took the test with a time limit than when they had unlimited time.

The following hypotheses were tested:

H0: μd = 0

Ha: μd > 0

The researchers analyzed the data and obtained the following output:

Which of the following is an appropriate conclusion based on the output?

**A **The data provide sufficient evidence to reject H0. Thus, the researchers conclude that sixth grade students get, on average, fewer correct answers and thus lower scores on math tests when taking them under timed conditions as compared to untimed conditions.

**B **The data provide sufficient evidence to reject H0. Thus, based on the data the researchers cannot conclude that mean number of correct answers on the math test for the timed condition is lower than for the untimed condition.

**C**The data do not provide sufficient evidence to reject H0. Thus, the researchers conclude that sixth grade students get, on average, fewer correct answers and, thus, lower scores, on math tests, when taking them under timed conditions as compared to untimed conditions.

D. The data do not provide sufficient evidence to reject H0. Thus, based on the data, the researchers cannot conclude that mean number of correct answers on the math test for the timed condition is lower than for the untimed condition.

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