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.

Suppose school has figured out a way to deliver the lectures all around the world in a way that creates a demand for their lectures because in some way they're better than the lectures that you could get from other universities. They evaluate the demand in Korea and demand in Germany. The demands are as follows: PK = 5,000 – 0.5QK PG = 3,000 – 0.5QG where PK and PG are the prices per course (per student) in Korea and Germany, respectively, and QK and QG are the number of students in Korea and Germany willing to enroll at those prices, respectively. The cost of online delivery is C = 1,800Q, where Q is the total number of students enrolled (i.e., Q = QK + QG). If school has decided to charge the same (uniform) tuition (price) to their online students everywhere around the world,

1. What price would they charge?

2. What would be their total online enrollment?

3. What would be their enrollment in Germany?

4. What would be their enrollment in Korea?

5. What would be the combined surplus in all the markets? I.e., what is the sum of the consumer surplus in Korea, consumer surplus in Germany, and school’s producer surplus from selling the instruction in both countries?

a.) A sociology professor has created a new assessment of political awareness. In using the assessment, she has determined that political awareness is normally distributed in college students with a population mean of 35.3 and a population standard deviation of 8.6.

Using the z-score found for the question above, what proportion of the population falls below a score of 22 on this test? Round your answer to four decimal places.

b.) A sociology professor has created a new assessment of political awareness. In using the assessment, she has determined that political awareness is normally distributed in college students with a population mean of 35.3 and a population standard deviation of 8.6.

What is the z-score for a student who gets a 43 on this test?

c.) A sociology professor has created a new assessment of political awareness. In using the assessment, she has determined that political awareness is normally distributed in college students with a population mean of 35.3 and a population standard deviation of 8.6.

Using the z-score found for the question above, what proportion of the population falls below a score of 43 on this test?

d.) What proportion of the normal distribution is below a z-score of -1.69. Round your answer to four decimal places.

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!

1.

You are conducting a study of students doing work-study jobs on your campus. Among the questions on the survey on the instrument are:

A. How many hours are you scheduled to work each week? Answer to the nearest hour.

B. How applicable is this work experience to your future employment goals?

Respond using the following scale: 1 = not at all, 2 = somewhat, 3 =very

Be sure to label the question you are working on:

a. Suppose you take random samples from the following groups: freshman, sophomores, juniors, and seniors. What type of sampling technique was used?

b. Describe the individuals of the study.

c. What is the variable for question A? What type of variable is it (quantitative or qualitative)? What is the level of measurement?

d. What is the variable for question B? What type of variable is it (quantitative or qualitative)? What is the level of measurement?

e. Is the proportion of responses “3=very” to question B a statistic or a parameter?

f. Suppose only 40% of the students you selected for the sample respond. What is the nonresponse rate? Do you think the nonresponse rate might introduce bias into the study? Explain.

g. Would it be appropriate to generalize the results of your study to all work-study students in the nation? Explain.