Practice Questions 7.1

Please match the following questions with their answers for the t-equation to convert a sample average into a standardized value:




A. What goes in the denominator?
B. What goes in the numerator?

__ The location of the sample average (adjusted for mu).
__ The spread of the sample average.

Please choose the location and spread for the t-equation for a dependent two-sample situation.

A. The location of the difference column: 
B. The spread of the difference column: 
C. The location of the sample average: (x̄-μ)
D. The spread of the sample average: (s/ √n)

Please choose the location and spread for the t-equation for an independent two-sample situation.

A. The location of the column of differences: ((x̄1-x̄2))
B. The two spreads combined together: (√(s^2/n1)+(s^2/n2))
C. The difference in the two locations: x̄1 - x̄2
D. The two spreads added together: ((S1/√n1) + (s2/√n2))

What are the two most significant ways that two-sample situations differ from one-sample situations?

A. Step A: Abstract is much more difficult.
B. The two locations can be the same or different. 
C. There are twice as many sources of variation in the situation.
D. The two spreads can be the same or different.

Use the information below to determine the dependency of the situation.

An instructor teaches a large statistics course at a local university and wonders how this semester's students will do. Before the semester starts, she randomly samples 50 of her students and gives them a pretest. After the semester is over, she gives the same students a post test. She calculates the difference in scores to see how well her students did that semester.

A.  This is a dependent two-sample situation.
B. This is a one-sample situation.
C. This is an independent two-sample situation.
D. This is a quasi-dependent two-sample situation.

Use the information below to determine the dependency of the situation.

An instructor teaches a large statistics course at a local university and wonders how this semester's students will do. Before the semester starts, she randomly samples 50 of her students and gives them a pretest. After the semester is over, she randomly samples 50 other students and gives them a post test. She calculates the difference in scores to see how well her students did that semester.

A. This is a quasi-dependent two-sample situation.
B. This is a dependent two-sample situation.
C. ~This is a rational dependent two-sample situation.
D. This is an independent two-sample situation.

Use the information below to determine the dependency of the situation.

A researcher in marital relationships wants to study the difference in opinion between husbands and wives. To get information on this issue she randomly selects 50 husbands and randomly selects 50 wives. She then gives them a survey of questions designed to answer her question.

A. This is an independent two-sample situation between husbands and wives.
B. This is a dependent two-sample situation between husbands and wives.
C. This is a relational-dependent between the husbands and the wives.
D. This is a quasi-dependent two-sample situation between the husbands and the wives.

Use the information below to determine the dependency of the situation.

A nutritionist questions whether two soft drinks have the same effect on weight gain in teenagers who consume a lot of soft drinks. To find out, she randomly selects 50 teenagers and asks them to drink only soft drink #1 for six weeks. She then measures the change in weight for each teenager. Next, she asks the same teenagers to drink only soft drink #2 for six weeks, and measures the change in weight for each teenager.

A. This is a dependent two-sample situation between teenagers drinking soft drinks.
B. This is an independent two-sample situation between teenagers drinking soft drinks.
C. This situation is dependent on the teenagers drinking a lot of soft drink.
D. This situation is independent of what the teenager's parents think.

What logic is used in statistics to make it possible to test for the population mean in a dependent two-sample situation?

A. Remove the dependency by adding the two data values to convert it to a one-sample situation.
B. Remove the dependency by changing the sampling design and repeating the experiment.
C. Ignore the dependency and use caution in the interpretation of the results.
D. Remove the dependency by subtracting the two data values to convert it to a one-sample situation.

Why is removing the dependency a reasonable option in a dependent one-sample situation?

A.  Because it is both logically and mathematically correct and easy to do.
B. Because the dependency is a perception and is not real.
C. Because every other method was much more complicated and difficult to perform.
D. Because adding dependency made a more complicated situation to understand and solve.

Why does a dependent two-sample situation have two sources of variation?

A. Because both "d bar" and "s_d" can verry from sample to sample
B. Because both s₁ and s₂ can vary from sample to sample
C. Because both x̄1 and x̄2 can vary from sample to sample
D. Because the difference between "d bar" and "s_d" can vary from sample to sample

What is the appropriate degrees of freedom to use for an independent two-sample situation where the variances are known to be equal.

A. The pooled degrees of freedom.
B. Satterthwaite's approximate degrees of freedom.
C. The unpooled degrees of freedom.
D. Welch's approximate degrees of freedom.

What is the appropriate degrees of freedom to use for a independent two-sample situation where the variances are known to be not equal.

A. Welch's approximate degrees of freedom if Satterthwaite's is given in the problem.
B. The pooled degrees of freedom.
C.  Satterthwaite's approximate degrees of freedom if given in the problem.
D. The unpooled degrees of freedom.

If Satterthwaite's degrees of freedom is given in the problem, why use it over Welch's degrees of freedom.

A.  Because Satterthwaite's is a much, much better approximation than Welch's.
B. Because Satterthwaite's is a much more complicated approximation than Welch's.
C. Because Welch's approximation has fallen out of favor in the field of statistics.
D. Because Satterthwaite's is a newer approximation than Welch's.

What is the appropriate equation for a dependent two-sample t-test?

What is the appropriate equation for an independent two-sample t-test?

What statistical method is used to tell if two population variances are equal, or not equal?

A. Visible observation by just looking at the two variances.
B. Tukey's Equality of Variance Test.
C.  Levene's Equality of Variance Test. 
D. Satterthwaite's Equality of Variance Test.

How is Levene's equality of variance test to be interpreted?

A. Levene's can best be interpreted using a Levene's table.
B.   Levene's is a hypothesis test best interpreted using the p-value approach.
C. Levene's is a confidence interval best interpreted using the mu-in-the-barn method.
D. Levene's is best interpreted using a Schematic Curve for the Levene's distribution.

How is a conclusion made in the Levene's equality of variance test?

A. A Levene's p-value greater than 1.00  means that the two population variances are equal.
B. Finding the Levene's p-value in the Levene's table tells if the two population variances are equal, or not.
C.  A p-value less than 0.05 means that the two population variances are not equal.
D. A p-value greater than 0.05 means that the two population variances are not equal.

How is a pooled sample variance calculated?

In statistics, what is the advantage of pooling information?

A. Pooling means comparing two pieces of information and selecting the better piece.
B.  By pooling, two pieces of information about a population can be combined into one better piece of information.
C. Pooling information is a way to reduce the numbers that must be accounted for.
D. By pooling, two sample statistics can be combined into one population parameter.