two skaters collide and embrace, in a completely inelastic collision. boomer, whose mass is 83 kg, is originally moving east with v=6.2km/hr. sooner whose. mass is 55kg, is originally moving north with v=7.8km/hr. (a) what is the velocity of the couple after impact? (b) what is the velocity of the center of mass of two skaters before and aafter collision? (c) what is the fractional change in the Kinect energy of the skaters because of the collision?

More than 100 million people around the world are not getting enough sleep; the average adult needs between 7.5 and 8 hours of sleep per night. College students are particularly at risk of not getting enough shut-eye.

A recent survey of several thousand college students indicated that the total hours of sleep time per night, denoted by the random variable X, can be approximated by a normal model with E(X) = 6.94 hours and SD(X) = 1.14 hours.

Question 1: Find the probability that the hours of sleep per night for a random sample of 4 college students has a mean x between 6.68 and 6.9.

Question 2: Find the probability that the hours of sleep per night for a random sample of 16 college students has a mean x between 6.68 and 6.9.

Question 3: Find the probability that the hours of sleep per night for a random sample of 25 college students has a mean x between 6.68 and 6.9.

2. Mr.Jones suspects that the majority of his students (more than a proportion of .5) prefer projects to exams. He decides to conduct a hypothesis test to investigate this. He asks a random sample of 25 students whether they prefer projects or exams and 14 of them say they prefer projects. Use this information to answer the following questions.

a. (2 points) What is the null hypothesis about the proportion of students that prefer projects?

b. (2 points) What is the alternative hypothesis about the proportion of students that prefer projects?

c. (2 points) What is the sample proportion?

d. (2 points) What is the standard score (z statistic) for the sample proportion?

e. (2 points) What is the P-value?

f. (2 points) Should he reject the null hypothesis at the 5% significance level?

g. (2 points) Based on your answer to part (f), does he have sufficient evidence to conclude that the majority of students prefer projects to exams?

Test the indicated claim about the means of two populations. Assume that the two samples are independent simple random samples selected from normally distributed populations. 1) A researcher was interested in comparing the GPAs of students at two different colleges. Independent random samples of 8 students from college A and 13 students from college B yielded the following GPAs: College A College B 3.7 3.8 2.8 3.2 3.2 4.0 3.0 3.0 3.6 2.5 3.9 2.6 2.7 3.8 4.0 3.6 2.5 3.6 2.8 3.9 3.4 Use a 0.10 significance level to test the claim that the mean GPA of students at college A is different from the mean GPA of students at college B. (Note: x1 = 3.1125, x2 = 3.4385, s1 = 0.4357, s2 = 0.5485.) Make sure to include all steps of a hypothesis test in your answer.

STEP 1:

STEP 2:

STEP 3:

STEP 4:

STEP 5:

STEP 6:

A. To compute a student's Grade Point Average (GPA) for a term, the student's grades for each course are weighted by the number of credits for the course. Suppose a student had these grades:
3.6 in a 5 credit Math course
2.2 in a 2 credit Music course
2.6 in a 5 credit Chemistry course
3.1 in a 4 credit Journalism course
What is the student's GPA for that term? Round to two decimal places.

B) For a 4-unit class like Statistics, students should spend average of 12 hours studying for the class. A survey was done on 23 students, and the distribution of total study hours per week is bell-shaped with a mean of 13 hours and a standard deviation of 2.8 hours.

Use the Empirical Rule to answer the following questions.

i) 68% of the students spend between__hours and__hours on Statistics each week.

ii) 95% of the students spend between__hours and__hours on Statistics each week.

iii) 99.7% of the students spend between__hours and__hours on Statistics each week.

As reported in College Teaching, in a 2006 article entitled “Humor in Pedagogy: How Ha-Ha Can Lead to Aha” (Vol. 54, Issue 1), R. L. Garner randomly assigned 117 undergraduates to “review lecture videos” on statistics research methods. The videos either did or did not have short bits of humor inserted. Students who viewed the humor-added version of the video gave significantly higher ratings in their opinion of the lesson, how well the lesson communicated information, and the quality of the instructor. Even more importantly, that same group of students also recalled and retained significantly more information on the topic.

Determine whether each variable is an explanatory variable or a response variable.

Enter the number of the term that corresponds to each choice:

1. Students' opinion of lesson
2. Students' rating of the quality of instructor
3. Humor condition of the video (i.e., with or without short bits of humor)
4. Students' ratings of how well lesson communicated information

Is this an experiment? y/n

Conscientiousness is a trait which implies discipline, dependability, and a heightened sense of personal responsibility. A school administrator wants to compare conscientiousness between high school and university students. He recruits 10 university and 15 high school students and measures their conscientiousness scores on a scale from 1 to 20 where 20 indicates greater conscientiousness. The university students have a mean conscientiousness score of 10 with a standard deviation of 1.5. The high school students have a mean conscientiousness score of 8 with a standard deviation of 1.7. In addition, standard error = .646. Is there a difference in conscientiousness between high school and university students?

a. Identify the IV, IV levels, and DV.

IV:
Levels:
DV:

b. Is this experiment a paired-samples or independent-samples design?

c. State null and alternative hypotheses in words.

H₀:
H₁:

d. Conduct a statistical test of the hypothesis

t( ) =

e. Decide whether to reject or retain the null hypothesis.

f. Interpret your results.

Conscientiousness is a trait which implies discipline, dependability, and a heightened sense of personal responsibility. A school administrator wants to compare conscientiousness between high school and university students. He recruits 10 university and 15 high school students and measures their conscientiousness scores on a scale from 1 to 20 where 20 indicates greater conscientiousness. The university students have a mean conscientiousness score of 10 with a standard deviation of 1.5. The high school students have a mean conscientiousness score of 8 with a standard deviation of 1.7. In addition, standard error = .646. Is there a difference in conscientiousness between high school and university students?

a. Identify the IV, IV levels, and DV.

IV:
Levels:
DV:

b. Is this experiment a paired-samples or independent-samples design?

c. State null and alternative hypotheses in words.

H₀:
H₁:

d. Conduct a statistical test of the hypothesis

t( ) =

e. Decide whether to reject or retain the null hypothesis.

f. Interpret your results.

Suppose a video teaching method will be adopted if a hypothesis test supports the conclusion that the video teaching method increases the mean grade point average (GPA) of students. Now, the mean GPA of students for the current face-to face teaching method is 3.04. Which of the following is FALSE?

Select one:

a. At the 0.05 level of significance, the video teaching method will be adopted if the sample mean GPA for the video teaching method is found to be higher than 3.04

b. Type I error may be made when the hypothesis test concludes that the video teaching method will be adopted but actually the mean GPA of students for the video teaching method does not increase the GPA of students for the current face-to-face teaching method.

c. In this hypothesis test, H0: µ ≤ 3.04 vs H₁:  µ > 3.04

d. Type II error may be made when the hypothesis test concludes that the video teaching method will not be adopted but actually the mean GPA of students for the video teaching method is higher than 3.04.