1. Below are several research scenarios. Indicate which set of statistical analyses should be used to analyze the data collected in study, and explain why that statistical test should be used

(a) Teachers at a local middle school were interested in exploring the effects of a collaborative peer teaching program on the motivation levels of seventh-grade students. Four of eight classes of seventh grade students were randomly selected at Bulloch Middle School to serve as subjects in this study. Students within each class were then randomly assigned to one of three groups: a collaborative peer teaching program, group learning activities, or individual learning activities. Each class was taught by a different teacher. The Middleman motivation scale was used to measure motivation in the subjects, and this scale produces scores that range from 1 to 25 with higher scores indicating greater motivation. Validity for the Middleman scale was previously ascertained by examining how scores from the Middleman motivation scale corresponded to scores from variables that are theoretically related to motivation, such as effort to achieve, persistence, intelligence, and self-efficacy. Internal consistency for scores from the Middleman scale typically range between .81 and .86. Data for the current study were collected at the end of a 16 week program. Analysis of these data revealed that students in the individual learning activities demonstrated a statistically higher level of motivation compared with students in the two other, traditional groups .

A student at a junior college conducted a survey of 20 randomly selected? full-time students to determine the relation between the number of hours of video game playing each? week, x, and? grade-point average, y. She found that a linear relation exists between the two variables. The? least-squares regression line that describes this relation is y = -0.0503x + 2.9381.

(a) Predict the grade-point average of a student who plays video games 8 hours per week. The predicted grade-point average is ___ (round to the nearest hundredth as needed.)

(b) Interpret the slope. For each additional hour that a student spends playing video games in a week, the grade-point average will increase or decrease, by _ points, on average.

(c) If appropriate, interprety the y-intercept. A) The average number of video games played in a week by students is 2.9443 B) The grade-point average of a student who does not play video games is 2.9443 C) It cannot be interpreted without more information.

(d) A student who plays video games 7 hours per week has a grade-point average of 2.64. Is the students grade-point average above or below average among all students who play video games 7 hours per week? The students grade-point average is above or below average for those who play video games 7 hours per week.

Among the budget cuts that the city council is considering is a 5 percent reduction in funds for secondary education. As the principal of one of the junior high schools that could be affected, Stella is worried. Such a reduction would almost certainly mean teacher layoffs and fewer teachers teaching more students.

Currently the school offers basic math and english courses for students on three levels: average, below average, and above average. However, a smaller budget may require offering only two levels next year. One possibility that Stella is considering is dropping the accelerated courses. After all, the bright kids would do well no matter what. On the other hand, dropping courses designed for below average student would mean that those students would not get the extra attention that they need. Stella think that if push comes to shove,its the honors program that will have to go.

Answer the following questions:

1 - What solution would you offer if you were Stella and there were budget cuts in your school?

2 - Is Stella right that bright kids will do well no matter what? Explain your answer.

3 - At what age is intelligence set? Is there anything you can do to improve your intelligence score on an IQ test?

4 - Should gifted students and below average students be integrated into the same class? Explain.

SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.

SCENARIO 8-3

To become an actuary, it is necessary to pass a series of 10 dogs, including the most important one, an dog in probability and statistics. An insurance company wants to estimate the mean score on this dog for actuarial students who have enrolled in a special study program. They take a sample of 8 actuarial students in this program and determine that their scores are: 2, 5, 8, 8, 7, 6, 5, and 7. This sample will be used to calculate a 90% confidence interval for the mean score for actuarial students in the special study program.

17) Referring to Scenario 8-3, a 90% confidence interval for the mean score of actuarial students in the special program is from ________ to ________.    17) _____________

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.

18) True or False: Referring to Scenario 8-3, for the confidence interval to be valid, it is necessary that test scores of students in the special study program on the actuarial dog be normally distributed.    18) ______

A) True                       B) False

25) True or False: Referring to Scenario 8-6, this interval requires the use of the t distribution to obtain the confidence coefficient. 25) ______

A) True           B) False

28) True or False: Referring to Scenario 8-6, it is possible that the true proportion of people that recognize the product is between 0.36 and 0.54.           28) ______

A) True                       B) False

For the scenarios answer the following:

a. State the independent (or quasi-independent) variable

b. State the dependent variable

c. Should the alternative hypothesis be one-tailed or two-tailed? Explain why.

d. State the null hypothesis

e. State the appropriate alternative hypothesis.

Scenarios1)  A researcher is interested in determining if there is a difference in the amount of time college students spend texting during class depending on where they sit in a classroom. He video tapes three different classrooms on campus and records the amount of time students in the front (first two rows), students in the middle (middle two rows) and students in the back (last two rows) of the classroom spend texting during the 45-minute lecture.

Scenario2) Ms. Nosienelly believes that adults will make more voice calls on their cell phone in public than adolescents will. To test her idea she asks a group of 100 fifteen-year-olds and a group of 100 forty-five-year-olds how many times a day they make a voice call on their cell phone while they are in public.

Scenario3) A university professor wanted to know if the way students were tested made a difference in their grades. One class took all their exams on a computer while a second class took all their exams on paper. The exact same exams were used for both groups. The grades on the exams were compared to see which group performed better

There is a lot of interest in the relationship between studying music and studying math. We will look at some sample data that investigates this relationship. Below are the Math SAT scores from 8 students who studied music through high school and 11 students who did not. Test the claim that students who study music in high school have a higher average Math SAT score than those who do not. Test this claim at the 0.05 significance level.

The 8 students who studied music in high school (x₁)

The 11 students who did not study music in high school (x₂)

If you are using software, you should be able copy and paste the data.

(b) Use software to calculate the test statistic or use the formula

t =

(c) Use software to calculate the degrees of freedom (d.f.) or use the formula

Round your answer to the nearest whole number.
d.f. =   

(d) What is the critical value of t? Use the answer found in the t-table or round to 3 decimal places.
t_α =  

The Weschler Intelligence Scale for Children (WISC) is an intelligence test designed for children between the ages of 6 and 16. The test is standardized so that the mean score for all children is 100 and the standard deviation is 15. Suppose that the administrators of a very large and competitive school district wish to estimate the mean WISC score for all students enrolled in their programs for gifted and talented children. They obtained a random sample of 40 students currently enrolled in at least one program for gifted and talented children. The test scores for this sample are as follows: 94,106,123,111,127,112,132,107,123,115,133,132,121,109,121,110,107,128,104,118, 111,127,108,119,121,122,102,130,97,111,125,114,99,101,123,124,108,116,144,113 Click to download the data in your preferred format. CrunchIt! CSV Excel JMP Mac Text Minitab PC Text R SPSS TI Calc Use this data to calculate the mean WISC score, ?⎯⎯⎯ , for these 40 students. Next, compute the standard deviation, SD, of the sampling distribution of the sample mean, assuming that the standard deviation of WISC scores for students in the district is the same as for the population as a whole. Finally, determine both the lower and upper limits of a 90% ?-confidence interval for ? , the mean score for all students in the school district who are enrolled in gifted and talented programs. Give ?⎯⎯⎯ and the limits of the confidence interval precise to one decimal place, but give the standard deviation to at least three decimal places in order avoid rounding errors when computing the limits.

x=

SD =

Lower limit =

Upper limit =

Suppose the scores of a certain high school diploma test follow a normal distribution in the population with a mean of 195 and standard deviation of 30.

1. About ______ percent of the students have a score between 135 and 195.

2. About ______ percent of the students have a score between 225 and 255.

3. The middle 95% of the students have a score between ________  and ________   .

4. Recently class A just had a Math exam, but class B had a Verbal exam.

- Joe in class A has a math score of 160, and all the math scores in class A have a mean of 140 and a standard deviation of 10.

- Eric in class B has a verbal score of 80, and all the verbal scores in class B have a mean of 50 and a standard deviation of 12.

Let’s assume students in classes A and B have very similar academic background, and both classes are hugh classes with lots of students. Then roughly speaking, relative to their respective classmates, who did better in the recent exam, Joe or Eric?

5. A sample consists of 26 scores. What is the degrees of freedom for the sample standard deviation?​

(High school busing problem) The Arden County, Maryland, superintendent of education is responsible for assigning students to the three high schools in his county. He recognizes the need to bus a certain number of students, for several sectors of the county are beyond walking distance to a school. The superintendent               partitions the county into three geographic sectors as he attempts to establish a plan that will minimize the total         number of student miles traveled by bus. He also recognizes that if a student happens to live in a certain sector             and is assigned to the high school in that sector, there is no need to bus that student because he or she can walk               to school. The three schools are located in sectors B, C, and D.

              The following table reflects the number of high-school-age students living in each sector and the distance in               miles from each sector to each school:

              Each high school has a capacity of 500 students. Please define variables and set up the objective function and constraints of this problem using Linear Programming (LP) so that the total number of student miles traveled by bus is minimized. (5 points)