Two random samples are taken, one from among first-year students and the other from among fourth-year students at a public university. Both samples are asked if they favor modifying the student Honor Code. A summary of the sample sizes and number of each group answering "yes'' are given below:

First-Years (Pop. 1):n1=93 x2=56

Fourth-Years (Pop. 2):,n2=97 x1=62

Is there evidence, at an α=0.07 level of significance, to conclude that there is a difference in proportions between first-years and fourth-years? Carry out an appropriate hypothesis test, filling in the information requested.

A. The value of the standardized test statistic:

B. The P-value is

A statistics teacher believes that the final exam grades for her business statistics class have a normal distribution with a mean of 82 and a standard deviation of 8.

(1)Find the score which separates the top 10% of the scores from the lowest 90% of the scores.

(2)

The teacher plans to give all students who score in the top 10% of scores an A. Will a student who scored a 90 on the exam receive an A? Explain.

(3)

Find the score which separates the lowest 20% of the scores from the highest 80% of the scores.
(4)

The teacher plans to give all students who score in the lowest 10% of score an F. Will a student who scored a 65 on the exam receive an F? Explain.

1. Professor Bailey wanted to assess his students’ understanding of statistics. He decided to test both their problem- solving ability, and their conceptual understanding of basic statistics principles governing the topics they had covered so far. He gave his class 2 tests. Test 1 involved problem-solving using statistics formulas and test 2 was conceptual (i.e. it involved students interpreting statistical concepts). The mean on both tests was 70%. However, the standard deviation for the problem-solving test was 5, and the standard deviation for the conceptual test was 10. Based on the information given for both tests, how would you interpret the general performance/ test scores of the class in statistics? Explain your answer.

The Schiffert Health Center at Virginia Tech wants to see whether putting antibacterial soap in the dormitory bathrooms will reduce the number of visits to the infirmary. VT has 47 on-campus residence halls. They are home for 9300 students. Twenty residence halls have been randomly selected. In all 2,000 students spanning over all selected halls. Half of the dormitories are chosen at random and supplied with the special soap; the remaining ones were supplied with regular soap. At the end of the semester, the two types of soap are compared using the number of visits to the infirmary per person per semester.

1. After the data are analyzed, can we generalize our results to the 47 dormitories (population) and why?

Decisions about alpha level may be different, especially as it relates from hard sciences to social sciences. For example, a medical trial for cancer treatments conducts their statistical tests at .0001 – so for every 1 out of 10,000 patients, there may be issues, sickness or even death. For social science, we use alpha .05. We are comfortable with performing research, for example, on students. So we are satisfied with losing 5 out of 100 students or having our results being incorrect 5 out of 100 times. Do you agree with these alpha levels? Why or why not? What if your child’s education and the teacher assigned to him/her would be successful 95 out of 100 times?

In Professor Krugman’s economics course, the correlation between the students’ total scores prior to the final exam and their final exam scores is r = 0.7. The pre-final-exam totals for all students in the course have a mean of 265 and a standard deviation of 45. The final exam scores have mean of 76 and standard deviation 9. Professor Krugman has lost Sam’s final exam, but knows that her total before the exam was 290. He decides to predict her final-exam score from her pre-exam total. Use the least-squares best-fit regression line to predict Julie’s final-exam score. Round your answer to one decimal place.

A professor of a introductory statistics class has stated that, historically, the distribution of final exam grades in the course resemble a normal distribution with a mean final exam mark of 60% and a standard deviation of 9%.
(a) What is the probability that a randomly chosen final exam mark in this course will be at least 75%?
(b) In order to pass this course, a student must have a final exam mark of at least 50%. What proportion of students will not pass the statistics final exam?
(c) The top 2% of students writing the final exam will receive a letter grade of at least an A in the course. To four decimal places, find the minimum final exam mark needed on the statistics final to earn a letter grade of at least an A in the course.

Statistics))

1.The Round-trip-time between the college and home for a student is normally distributed with a mean of 47 min and a standard deviation of 4.6 min. To one-decimal place, what Round-trip-time would be considered the 70th percentile? Make sure to include units.

2.A recent study showed that the average amount of time spent doing part time job by students at a college is 29 hours per week with a standard deviation of 3.8 hours. If 64 students were selected at random, what is the probability that their average weekly working hours will be less than 20 hours?Round answer to two decimals, if necessary.Express answer in percent. Don't forget to put % sign with you answer.

COIN TOSSES In a large class of introductory Statistics students, the professor has each student toss a coin 16 times and calculate the proportion of his or her tosses that were heads. The students then report their results, and the professor plots a histogram of these several proportions.

1. What shape would you expect this histogram to be? Why?

2. Where do you expect the histogram to be centred?

3. How much variability would you expect among these proportions?

4. Explain why a Normal model should not be used here.

The answer is

1, symmetric

2, 0.5

3, 0.125

4. np=8<10

Please explain why the third question has answer 0.125. how did you get it?