1. A poll was taken of UW students to estimate the proportion of all students that believe the Husky men’s basketball team will beat Oregon at the upcoming game on 18 January. A random sample of 1,000students was selected, and via an emailed survey link, students were simply asked, Yes or No, if they thought the Huskies would win the game. Of the 1,000 students that were emailed, 200 chose not to answer. Of those that answered, 623 believe the Huskies will win.
2. 1. a) What is the sample size for the survey?
   2. b) What sample size would be needed to reduce the margin of error by one-half?

A statistics class for engineers consists of 53 students. The students in the class are classified based on their college major and sex as shown in the following contingency table:

If a student is selected at random from the class by the instructor to answer a question, find the following probabilities. Report your answer to 4 decimal places. (total 80 points)

Consider the following events:

A: The selected student is a male.

B: The selected student is industrial engineering major.

C: The selected student is civil engineering major.

D: The selected student is electrical engineering major.

Note: Indicate the type of probability as marginal, joint or conditional when asked.

Find the probability that the randomly selected student is a male. Indicate the type of probability. (8 + 2 = 10 points)

Find the probability that the randomly selected student is industrial engineering major. Indicate the type of probability. (8 + 2 = 10 points)

Find the probability that the randomly selected student is male industrial engineering major. Indicate the type of probability. (8 + 2 = 10 points)

Given that the selected student is industrial engineering major, what is the probability that the student is male? Indicate the type of probability.

(8 + 2 = 10 points)

Based on your answers on part a and d, are sex and college major of students in this class independent? Provide a mathematical argument? (6 points)

Consider the events A and B. Are sex and college major mutually exclusive events? Provide a mathematical argument to justify your answer. (6 points)

Find the probability that the randomly selected student is male or industrial engineering college major. (10 points)

Consider the events C and D. Are college major mutually exclusive events? Provide a mathematical argument to justify your answer. (6 points)

Find the probability that the randomly selected student is civil or electrical engineering college major. (6 points)

What is the probability that a randomly selected student is neither a male nor an industrial engineering college major? (6 points)

SIU is a university in the UK catering for international students. There are currently 950 students. Fees were £16,000 for the last year and the president is concerned that adverse changes in the economic and educational environment are threatening the university’s future. The income of the market is expected to decline next year by 2%, and it is also expected that the average fee of competitive institutions will fall from £14,000 to £12,000. 10% of revenue is currently spent on promotion. The president does some research and estimates that the relevant demand elasticities are as follows:

PED = -1.6, YED = 2.2, AED = 1.8, CED = 0.8.

1. Estimate the number of students at the university next year, and revenue, if the president keeps the present marketing mix unchanged.
2. Estimate the level of fees that would have to be charged next year in order to maintain the number of students at its current level, assuming no change in promotion.
3. Estimate the level of fees that would have to be charged next year in order to reach the president’s target of 1,200 students.
4. If fees are maintained at their current level, estimate the amount that would need to be spent on promotion to achieve the target.
5. Determine which of the strategy options above is more profitable, assuming that these are the only alternatives under consideration.

f. Briefly outline other marketing mix options for achieving the target (50 words

A random sample of 250 students at a university finds that these students take a mean of 15.7 credit hours per quarter with a standard deviation of 1.5 credit hours. Estimate the mean credit hours taken by a student each quarter using a 98​% confidence interval.

Students at a certain school were​ surveyed, and it was estimated that 19​% of college students abstain from drinking alcohol. To estimate this proportion in your​ school, how large a random sample would you need to estimate it to within 0.08 with probability 0.99​, if before conducting the study​ (a) you are unwilling to predict the proportion value at your school and​ (b) you use the results from the surveyed school as a guideline.

a. n=

b. n=

2.5

7.In a survey of college​ students, each of the following was found. Of these​ students,

356356

owned a​ tablet,

294294

owned a​ laptop,

280280

owned a gaming​ system,

195195

owned a tablet and a​ laptop,

199199

owned a tablet and a gaming​ system,

137137

owned a laptop and a gaming​ system,

6868

owned a​ tablet, a​ laptop, and a gaming​ system, and

2626

owned none of these devices. Complete parts ​a) through ​e) below.

​a) How many college students were​ surveyed?

​(Simplify your​ answer.)

​b) Of the college students​ surveyed, how many owned a tablet and a gaming​ system, but not a​ laptop?

​(Simplify your​ answer.)

​c) Of the college students​ surveyed, how many owned a​ laptop, but neither a tablet nor a gaming​ system?

​(Simplify your​ answer.)

​d) Of the college students​ surveyed, how many owned exactly two of these​ devices?

​(Simplify your​ answer.)

​e) Of the college students​ surveyed, how many owned at least one of these​ devices?

​(Simplify your​ answer.)

4.

Thirty-five cities were researched to determine whether they had a professional sports​ team, a​ symphony, or a​ children's museum. Of these​ cities,

1919

had a professional sports​ team,

1717

had a​ symphony,

1414

had a​ children's museum,

1111

had a professional sports team and a​ symphony,

88

had a professional sports team and a​ children's museum,

66

had a symphony and a​ children's museum, and

44

had all three activities. Complete parts ​a) through ​e) below.

​a) How many of the cities surveyed had only a professional sports​ team?

​(Simplify your​ answer.)

​b) How many of the cities surveyed had a professional sports team and a​ symphony, but not a​ children's museum?

​(Simplify your​ answer.)

​c) How many of the cities surveyed had a professional sports team or a​ symphony

​(Simplify your​ answer.)

​d) How many of the cities surveyed had a professional sports team or a​ symphony, but not a​ children's museum?

​(Simplify your​ answer.)

​e) How many of the cities surveyed had exactly two of the​ activities?

​(Simplify your​ answer.)

3.2

7.

Construct the truth table for the compound statement q logical or left parenthesis p logical and tilde r right parenthesis .q ∨ (p ∧ ~r).

8.

Construct the truth table for the compound statement

left parenthesis p logical or tilde q right parenthesis logical or r(p ∨ ~q) ∨ r.

9.

Determine the symbolic form of the compound statement and construct a truth table for the symbolic expression. p ∨ (q ∨ r)

18.

Must the truth tables for

left parenthesis t logical and tilde s right parenthesis logical or tilde p(t ∧ ~s) ∨ ~p

and

left parenthesis s logical and tilde p right parenthesis logical or tilde t(s ∧ ~p) ∨ ~t

have the same number of trues in their answer​ columns?

Choose the correct answer below.

A.

​Yes, because the two expressions have exactly the same form and each term can be T or F regardless of which letter is being used or whether it is negated or not.

B.

​Yes, because the second expression contains the same three variables as the first expression.

C.

​No, the truth table for the first expression has 5 trues and the truth table for the second expression only has 3 trues.

D.

​No, because there is no relationship between the first expression and the second expression.

E.

​Yes, because half the answers for each expression will be true and half will be false.

In a large school, there are 60% students are athletes, 30% students in an honor program. 25% athlete students are in the honor program.

Let A = a randomly selected student is an athlete

B = a randomly selected student is in the honor program

Write the symbols of the following probabilities and find the value of the probabilities..

(a) The symbol for the probability a randomly selected athlete is in the honor program.

(b) The probability that a randomly selected student is an athlete and in the honor program.

(c) The probability that a randomly selected student is an athlete or is in the honor program.

(d) The probability that a randomly selected student is not an athlete.

1. In a study of habits of undergraduate students, a researcher sampled 53 students and found that the mean number of classes missed over the course of a school year was 18. Assume the population standard deviation, σ = 5.7.
   1. (5 points) Calculate the 95% confidence interval for the mean number of classes missed during the school year by undergraduate students.

2. (2 points) If the researcher had sampled 75 students, would the margin of error be larger or smaller?

3. (2 points) If the researcher used a 90% confidence level instead of 95%, would the margin of error be larger or smaller?

10. The grades of students are normal distributed. In a class of 10 students the average grade on a quiz is 16.35, with a standard deviation of 4.15. ( 3 marks ) a) Find the 90% confidence interval for the population mean grade. b) If you wanted a wider confidence interval, would you increase or decrease the confidence level?

Suppose that there are 100 students entering the Master’s of Business Administration program. Of these students, 20 have two years of work experience, 30 have three years of work experience, 15 have four years of work experience, and 35 have five or more years of work experience.

a) One of the students is selected at random. What is the probability that this student has at least three years of work experience?

b) The selected student has at least three years of work experience. What is the probability the student has four years of work experience?

c) Three students are selected at random. Calculate the probability that all three students have five or more years of work experience. Describe the key assumption required to make the calculation and comment on whether the assumption is reasonable.

d) Would it be reasonable to use the probability calculated in part a) as an estimate of the proportion of students entering the MBA degree program who have at least three years of work experience? Explain your answer. Limit your explanation to at most five sentences.