2. Behavior of wearing seat belt has two categories: Most Times or Always and Rarely or Never. Overall Grades for Undergraduate Degree has three categories: A or B, C, and D or F. In a group of 1534 students with grades A or B, 1354 students wear seat belts Most time or Always. In a group of 553 students with grade C, 428 students wear seat belts Most Time or Always. In a group of 105 students with grades D or F, 65 wear seat belts Most Time or Always. Conduct a test the hypothesis at 5% level of significance that Wearing seat belts and Grades at Undergraduate degree are independent or not. Show all four steps.

Descriptive analysis revealed that 68% of students passed Test 1. Suppose a random sample of 18 students is selected and defined ˆp as the proportion of students in the sample who passed Test 1.

Determine the mean of the sampling distribution of ˆp.
μˆp=

Determine the standard deviation of the sampling distribution of ˆp. Round the solution to six decimal places.
σˆp=

Determine the probability that between 63.3% and 77.3% of a random sample of 18 students passed Test 3. Round the solution to four decimal places.
P(0.633<ˆp<0.773) =

Determine the probability that less than 92.3% of a random sample of 18 students passed Test 3. Round the solution to four decimal places.
P(ˆp<0.923) =

The classrooms at the Redman Academy consist of cramped tables that seat 3 people. The probability of being-left handed is 26%, and left-handed test takers need to sit in the far-left seat, otherwise, they constantly bump elbows with the person next to them causing complaints.   
⦁   What is the probability that no one in a group of 3 students is left-handed?
⦁   What is the probability that only 1 person in the group of 3 students is left-handed?
⦁   What is the probability that no one at a table will complain during a test if I randomly seat three students?
⦁   I have 9 students in my class, 2 of which are left-handed. If I have exactly 3 tables and randomly seat the students, what is the probability of no complaints?

2. At a certain college, the student senate conducted a poll of 200 students to ask about using student services. In the poll, 24% of students had used tutoring services in the past week, 72% had used the library in the past week, and 14% had used both tutoring and the library in the past week.

a. What percent of students used either tutoring or the library in the past week?

b. What percent of students used neither tutoring nor the library in the past week?

c. What percent of students did not use the library? d. Given that a student visited the library, what is the probability that they used tutoring services?

d. That an instructor opposes the policy given that they teach in MSHP.

A testing center at the university wants to compare the average test taking time of undergraduate students on a standardized entrance exam to graduate school. Four departments are selected, and from each department, 25 students are randomly sampled (100 students total). The center then checks for test taking time (in minutes), and compares the average test taking time of students using ANOVA. Complete the following one-factor ANOVA summary table using alpha = .05. Based on the results, do students in different departments have different departments have different test taking times?

A teacher is interested in her students’ opinion on whether the non-required lecture is effective for them. She flips a coin every time a student walks into lecture and if it lands heads, she asks that student if they find lecture effective and records their answer.

(a) Are there any issues with creating a confidence interval with this sample if our parameter of interest is the proportion of enrolled students who find lecture effective? Explain briefly.

(b) Another lecturer asks a random sample of his students to comment on the efficacy of his lecture and fifty two (52) of the 80 students interviewed reported finding the lecture effective. Create a 98% confidence interval for the proportion of students who find his lecture effective.

Define vector addition as y_1⊕ y_2=y_1+y_2-3 and scalar multiplication as c ⊙y_1=cy_1-3c+3. Let V be the space of all solutions of the equation in problem 3 that uses the above definitions of vector addition and scalar multiplication. Use the Vector Space Definition to prove that V is a vector space

6.5 We have postulated an RGB model for the material properties of surfaces. Give
an argument for using a subtractive color model instead.

6.7 Show that if v lies in the same plane as l, n, and r, then the halfway angle
satisfies
2ψ = φ.
What relationship is there between the angles if v is not coplanar with the other
vectors?

If a platinum indicator electrode is used to measure [Cu²⁺] (standard reduction potential of Cu²⁺ is 0.337 V), and [Cu²⁺] = 0.0053 M, what is the cell potential (V) if the reference electrode is SCE and the measurement is taken at 298 K?

I have gotten .270 and .073, Im not sure what I am doing wrong