T2 Lecture Exercise 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?

A = The spread of the sample average. B = The location of the sample average (adjusted for mu).

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

A p-value less than 0.05 means that the two population variances are not equal.

In statistics, what is the advantage of pooling information?

By pooling, two pieces of information about a population can be combined into one better piece of information.

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

Levene's Equality of Variance Test.

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

Levene's is a hypothesis test best interpreted using the p-value approach.

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

Remove the dependency by subtracting the two data values to convert it to a one-sample situation.

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

Satterthwaite's approximate degrees of freedom if given in the problem.

Please choose the location and spread for the t-equation for an independent two-sample situation. The difference in the two locations (x1−x2) The two spreads combined together √(s1^2/n1)+(s2^2/n2) The location of the column of differences (x1−x2) The two spreads added together (S1/√n1)+(s2/√n2)

The difference in the two locations (x1−x2) The two spreads combined together √(s1^2/n1)+(s2^2/n2)

@Please choose the location and spread for the t-equation for a dependent two-sample situation. The location of the difference column d−0. The spread of the difference column sd/√η The location of the sample average(x−μ) The spread of the sample average s/√η

The location of the difference column d−0. The spread of the difference column sd/√η

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

The pooled degrees of freedom.

*What are the two most significant ways that two-sample situations differ from one-sample situations? There are twice as many sources of variation in the situation. The two spreads can be the same or different. The two locations can be the same or different. Step A: Abstract is much more difficult.

There are twice as many sources of variation in the situation. The two spreads can be the same or different.

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.

This is a dependent two-sample situation between teenagers drinking soft drinks.

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.

This is a dependent 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.

This is an independent two-sample situation between husbands and wives.

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.

This is an independent two-sample situation.

@How is a pooled sample variance calculated?

a

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

a

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

a/d

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

Because Satterthwaite's is a much, much better approximation than Welch's.

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

Because both 𝑑⎯ and 𝑠𝑑 can vary from sample to sample.

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

Because it is both logically and mathematically correct and easy to do.