Statistics Math 125 - Module 1 Homework 1.6

What is replication in an​ experiment?

Replication is applying each treatment to more than one experimental unit.

To help assess student learning in her developmental art ​courses, an art professor at a community college implemented​ pre- and​ post-tests for her developmental art students. A​ knowledge-gained score was obtained by taking the difference of the two test scores.

What type of experimental design is​ this? Matched pair What is the response variable in this​ experiment? Difference in test scores What is the​ treatment? Art course

Does the level of octane in gasoline affect gas​ mileage? To answer this​ question, an automotive engineer obtains 90 cars. Thirty of the cars are​ compact, 30 are full​ size, and 30 are sport utility vehicles​ (SUVs). Design an experiment for the engineer.

Randomized block design

Determine whether the following statement is true or false. ​Generally, the goal of an experiment is to determine the effect that the treatment will have on the response variable.

True

A school psychologist wants to test the effectiveness of a new method of teaching mathematics. She recruits 300 second​-grade students and randomly divides them into two groups. Group 1 is taught by means of the new​ method, while group 2 is taught by traditional methods. The same teacher is assigned to teach both groups. At the end of the​ year, an achievement test​ (graded on a scale from​ 1-10) is administered and the results of the two groups are compared. Complete parts​ (a) through​ (i) below

(a) What is the response variable in this​ experiment? The scores on the achievement tests of both group 1 and group 2 (b) Is the response variable qualitative or​ quantitative? The response variable is quantitative because it is a measurement. (c) Which of the following explanatory variables is​ manipulated? Method of teaching (d) What are the​ treatments? How many treatments are​ there? The treatments are the new teaching method and the traditional teaching method. There are 2 treatments. ​(e) How are the factors that are not controlled dealt​ with? Random assignment (f) Which group serves as the control​ group? Group 2 serves as the control group because this group corresponds to the standard method that will be compared to the other method. (g) What type of experimental design is​ this? Completely randomized design (h) Identify the subjects. The 300 students (i) Draw a diagram to illustrate the design. Choose the correct figure below. Random assign of students to treat. Group1 - New treatment Group2 - Traditional treatment. Compare scores.

Researchers wanted to evaluate whether a certain herb improved memory in elderly adults as measured by objective tests. To do​ this, they recruited 95 men and 128 women older than 60 years and in good health. Participants were randomly assigned to receive the​ herb, 40 mg 3 times a​ day, or a matching placebo. A measure of memory improvement was determined by a standardized test of learning and memory. After 6 weeks of​ treatment, the data indicated that the herb did not increase performance on standard tests of​ learning, memory,​ attention, and concentration. These data suggest​ that, when taken following the​ manufacturer's instructions, the herb provides no measurable increase in memory or related cognitive function to adults older than 60 years with healthy cognitive function. Complete parts​ (a) through​ (g) below.

(a) What type of experimental design is​ this? Completely randomized design (b) What is the population being​ studied? Adults older than 60 years and in good health ​(c) What is the response variable in this​ study? The score on the standardized test of learning and memory (d) What is the factor that is manipulated and fixed at a single​ level?The herb What are the​ treatments? 40 mg 3 times a day or a matching placebo ​(e) Identify the experimental units. Choose the correct answer below.​The 95 men and 128 women older than 60 who are in good health that participated in the study (f) What is the control group in this​ study?The placebo group serves as the control group because this group corresponds to the reference point that will be compared to the other group. (g) Draw a diagram to illustrate the design. Choose the correct figure below. Random assign of adults to treat. Group1 Herb, Group2 Placebo, Compare memory.

Researchers wanted to test the effectiveness of a new drug therapy for treating patients with dementia. To do​ this, they identified 135 patients with a diagnosis of dementia. Patients were randomly assigned to one of three treatment groups. Forty dash five patients were randomly assigned to receive the new drug​ therapy, another 45 received the older drug​ therapy, and the final 45 received a placebo therapy. To measure the effectiveness of the​ treatment, researchers scored each patient on a standardized rating scale for dementia. After collecting and comparing the scores for the three treatment​ groups, the researchers concluded that the new drug therapy is significantly more effective than both the older drug therapy and the placebo therapy in the treatment of dementia. Complete parts​ (a) through​ (f).

(a) What type of experimental design is​ this? Completely randomized design (b) What is the population being​ studied? All patients with a diagnosis of dementia ​(c) What is the response variable in this​ study?The score on the standardized rating scale for dementia (d) What are the​ treatment(s)?The new drug​ therapy, the older drug​ therapy, and the placebo therapy (e) Identify the experimental units. Choose the correct answer below.The 135 patients with a diagnosis of dementia (f) Which figure illustrates the design of this​ experiment? Randow assignment of adults to treatments. Group1 45patients New therapy, Group2 45patients Old therapy, Group3 45patients placebo therapy, Compare standardized rating scale scores.

Suppose you are interested in comparing brand A interior latex paint to brand B interior latex paint. Design an experiment to determine which paint is better for painting bathrooms.

Matched-pairs design because experimental units are paired up and there are only two levels of treatment.

A researcher has decided to test the effectivness of a drug meant to reduce high cholesterol through a completely randomized design. She has obtained 9 volunteers with high​ cholesterol: Amanda,​ Brian, Christine,​ David, Emily,​ Fred, George,​ Heather, and Ivan. Number the volunteers 1 through​ 9, alphabetically. Use the second row of digits in the random number table below to randomly assign 3 of the volunteers to the experimental group​ (ignore zeros). The remaining volunteers will go into the control group. List the individuals in each group.

What are the numbers of the three volunteers​ selected? 7, 6, 3 List the three indivduals assigned to the experimental group. Choose the correct answer below. George, Fred, Christine List the remaining indivduals assigned to the control group. Choose the correct answer below. Heather, Amanda, Ivan, David, Emily, Brian

A golf pro wanted to compare two types of golf clubs. One type is graphite dash shafted and the other is steel dash shafted. It is a common belief that graphite shafts give more distance. This belief is tested by having 10 golfers hit one ball with each type of club and then determining the distance that the ball traveled. A coin flip was used to determine which type of club each player would hit with first. Results indicated that there was no difference in the two types of club. Complete parts​ (a) through​ (f) below.

​(a) What type of experimental design is​ this?Matched-pairs design ​(b) What is the response variable in this​ study?The distance (c) What is the factor that is set to predetermined​ levels? What is the​ treatment?The factor is the type of club. The treatments are graphite dash shafted and steel dash shafted. ​(d) Identify the experimental units. Choose the correct answer below.The golfers ​(e) Why is a coin used to decide the club each player would hit with first​?To eliminate bias as to which club was used first (f)Draw a diagram to illustrate the design. Choose the correct figure below. Randomly assign each golfer to both treatments. Administer treatments ad record distances. For each golfer compare the distances.