Puzzle #1 A kindergarten teacher knows that exactly one of four students, Kathy, Andy, Jose, or Dana, took Amy’s cookie. When asked about who did it, Kathy said: “Andy did it.”, Andy said: “Dana did it.”, Jose said: “I didn’t do it.”, and Dana said: “Andy lied when he said I did it.” 1. If the teacher knows that exactly one of the students is telling the truth, who did it? Explain.

2. If the teacher knows that exactly one of the students is lying, who did it? Explain. Puzzle #2 There are three neighbors living in a row. Each house has a different color and a different animal and person living in/at the house. Each person has a different profession. The horse lives in the first house. The doctor is Jamal’s neighbor. Jamal does not have a ferret as a neighbor. Carlos does not live in the blue house and Jamal does not live in the green house. Ann is a lawyer and lives in the 3rd house. The professor has the horse as a neighbor. The mouse does not live in the red house. The lawyer does not live in the blue house. 1. Determine the color of the house the horse lives in. This project will be scored out of 10 points in the following way:

In a study of government financial aid for college​ students, it becomes necessary to estimate the percentage of​ full-time college students who earn a​ bachelor's degree in four years or less. Find the sample size needed to estimate that percentage. Use a 0.03 margin of error and use a confidence level of 95​%.

Complete parts​ (a) through​ (c) below. a. Assume that nothing is known about the percentage to be estimated. nequals nothing ​(Round up to the nearest​ integer.) b. Assume prior studies have shown that about 45​% of​ full-time students earn​ bachelor's degrees in four years or less. nequals nothing ​(Round up to the nearest​ integer.) c. Does the added knowledge in part​ (b) have much of an effect on the sample​ size? A. ​Yes, using the additional survey information from part​ (b) only slightly increases the sample size. B. ​No, using the additional survey information from part​ (b) does not change the sample size. C. ​Yes, using the additional survey information from part​ (b) dramatically reduces the sample size. D. ​No, using the additional survey information from part​ (b) only slightly reduces the sample size.

Consider the following fictional examples of correlations found in research. In each example, the researcher explains the correlation by inferring causality. For each example, please provide at least two other possible explanations as to why the relationship exists. Consider the reverse causality or other external variables in your explanation. Think critically and creatively!

1) A researcher finds that there is positive correlation between watching violence on T.V. and violent behavior in adolescence. He stipulates that watching violence on T.V. causes violent behavior in adolescents.

2) A research study determines that there is a negative correlation between GPA and number of sexual partners among college students. The researchers explain that studying more/having a higher GPA cause college students to be less sexually active.

3) A professor in a nursing program finds that students who choose to spend more of their rotation hours in an oncology ward rate higher on a scale that measures level of compassion. He postulates that training in an oncology ward causes increases in compassion levels.

4) A political science researcher finds that there is a negative correlation between level of education and amount of donation to political campaigns. She determines that getting a higher education causes decreased desire to donate to political campaigns.

For each question please state your null and alternative hypothesis, your p-value and conclusion of your hypothesis test. You may use your calculator to perform the hypothesis.

1. Research conducted a few years ago showed that 35% of UCLA students had travelled outside the US. UCLA has recently implemented a new study abroad program and results of a new survey show that out of the 100 randomly sampled students 40 have travelled abroad. Is there significant evidence to suggest that the proportion of students at UCLA who have travelled abroad has increased after the implementation of the study abroad program? Use a .01 significance level.

   2. Sleep experts believe that sleep apnea is more likely to occur in men than in the general population. In other words, they claim the percentage of men who suffer from sleep apnea is greater than 5.8%. To test this claim, one sleep expert examines a simple random sample of 90 men and determines 9 of these men suffer from sleep apnea. Does this evidence support the claim that the percentage of men who suffer from sleep apnea not longer equals 5.8%? Use a 0.05 level of significance.

Prof. Gersch knows that the amount of learning at YU is normally distributed with unknown mean and standard deviation of 2 hours.  He surveys a random sample of 16 students and find that the average amount of learning that these students do per week is 19 hours.
a) Construct a 95% CI for the true (pop) mean amount of learning.
b) How many students should Prof. Gersch have surveyed so that the maximum margin of error in his 95% CI was 2 hours?
c) Had someone told Prof. Gersch, prior to his sampling, that the true mean amount of learning was 18 hours per week, yet he thought the mean amount was greater, state the appropriate hypotheses and conduct the appropriate test at alpha of 0.05 using the sample evidence obtained.
Use all possible methods here!
Do the test also at alpha pf 0.01. What method is easier, why?
d) Had Prof. Gersch suspected instead that the true mean amount of time spent on studying was different than 18 hours, state the appropriate hypotheses and conduct the appropriate test at alpha of 0.05 using the sample evidence obtained. Use all the possible methods here!

Social networking is becoming more and more popular among school-going teenagers. Camden Research Group used a survey of students in several states to determine the percentage of students who use social networking sites. Assume that the results for surveys in Georgia, Maryland, Washington, and Wyoming are as follows.

Answer the following 6 questions.

1. We wish to conduct a hypothesis test to determine whether the proportion of students using social networking sites are equal for all four states. What is the value of your test statistic?

2. True or False: At least one state's population proportion is different from the others. (5% significance)

3. What is the sample proportion for Georgia?

4. Which state has the largest sample proportion?

5. Using the multiple comparison procedures, answer the following:

True or False: There is a significant difference between Georgia and Maryland. (5% significance)

6. Using the multiple comparison procedures, answer the following:

True or False: There is a significant difference between Wyoming and Maryland. (5% significance)

14-60.

Referring to Exercise 14-58, suppose a student has an SAT score of 400. What is her estimate GPA at State University? Discuss the ramifications of using the model developed in Exercise 14-58 to estimate this student’s GPA.

14-58

At State University, a study was done to establish whether a relationship exists between students’ graduating grade point average (GPA) and the SAT verbal score when the student originally entered the university. The sample data are reported as follows:

GPA    2.5 3.2 3.5 2.8 3.0 2.4 3.4 2.9 2.7 3.8

SAT    640 700 550 540 620 490 710 600 505 710

a. Develop a scatter plot for these data and describe what, if any, relationship exists between the two variables, GPA and SAT score.

b. (1) Compute the correlation coefficient. (2) Does it appear that the success of students at State University is related to the SAT verbal scores of those students? Conduct a statistical procedure to answer this question. Use a significance level of 0.01.

c. (1) Compute the regression equation based on these sample data if you wish to predict the university GPA using the student SAT score. (2) Interpret the regression coefficients.

1. The reading speed of Ms. Alayeb's second grade students is approximately normal, with a mean 60 WPM and a standard deviation of 10 WPM. (Please round your answer to 4 decimal places )

a) What is the probability a randomly selected student will read more than 65 WPM?

b)What is the probability that a random sample of 27 Ms. Alayeb's second grade students results in a mean reading rate of less than 56 WPM?

c)What is the probability that a random sample of 18 Ms. Alayeb's second grade students results in a mean reading rate of more than 63 WPM?

2. Slices of pizza for a certain brand of pizza have a mass that is approximately normally distributed with a mean of 66.5 grams and a standard deviation of 2.34 grams.

a) For samples of size 18 pizza slices, what is the standard deviation for the sampling distribution of the sample mean?

b) What is the probability of finding a random slice of pizza with a mass of less than 66.1 grams?

c) What is the probability of finding a 18 random slices of pizza with a mean mass of less than 66.1 grams?

d) What sample mean (for a sample of size 18) would represent the bottom 15% (the 15th percentile)?

Randomly selected students were given five seconds to estimate the value of a product of numbers with the results shown below.
Estimates from students given 1×2×3×4×5×6×7×81×2×3×4×5×6×7×8:

169, 500, 5635, 10000, 45000, 50, 5000, 800, 1000, 200169, 500, 5635, 10000, 45000, 50, 5000, 800, 1000, 200

Estimates from students given 8×7×6×5×4×3×2×18×7×6×5×4×3×2×1:

400, 40320, 500, 350, 450, 225, 1500, 428, 550, 40000400, 40320, 500, 350, 450, 225, 1500, 428, 550, 40000

Use a 0.050.05 significance level to test ?0:?21=?22H0:σ12=σ22 vs. ??:?21≠?22Ha:σ12≠σ22 :

(a) The test statistic is

(b) The larger critical value is

(c) The conclusion is
A. There is not sufficient evidence to reject the claim that the two populations have equal variances. (So, we can assume the variances are equal.)
B. There is sufficient evidence to reject of the claim that the two populations have equal variances. (So, we can assume the variances are unequal.)

Again, there is research on the relationship between gender and sense of direction. Recall that, in their study, the spatial orientation skills of 30 male and 30 female students were challenges in a wooded park near the Boston College campus in Newton, Massachusetts. The participants were asked to rate their own sense of direction as either good or poor.

In the park, students were instructed to point to predesignated landmarks and also to the direction of south. For the female students who had rated their sense of direction to be good, the table above provides the pointing errors (in degrees) when they attempted to point south.

1. If, on average, women who consider themselves to have a good sense of direction do not better than they would by just randomly guessing at the direction of south, what would their mean pointing error be?
2. At the 1% significance level, do the data provide sufficient evidence to conclude that women who consider themselves to have a good sense of direction really do better, on average, than they would by just randomly guessing at the direction of south? Use a one-mean t-test.
3. Obtain a normal probability plot, boxplot, or stem-and-leaf diagram of the data. Based on this plot, is use of the t-test reasonable? Explain your answer.