A marketing research professor is conducting a telephone survey and needs to contact at least 160 wives, 140 husbands, 110 single adult males, and 120 single adult females. It costs $2 to make a daytime call and $4 (because of higher labor costs) to make an evening call. The table shown below lists the expected results. For example, 10% of all daytime calls are answered by a single male, and 15% of all evening calls are answered by a single female. Because of a limited staff, at most half of all phone calls can be evening calls. Determine how to minimize the cost of completing the survey

Develop a Report for the following

1) State the decision variables and constraints in this problem.

Create a die, which will roll a 6 with probability of 50% and all other numbers (1-5) with equal probability. What is E(Y) if Y was the outcome of that die? and X is the result of the fair die.

sd(Y)

var(X-2Y)

Please write the code in R

When answering each of the following, the random variable Y is normally distributed with a mean of 65 and a standard deviation of 4.

1. The value of z for being able to determine P(Y ≤ 60) is _____

The P(Y ≤ 60) is _____

2. The 2 values of z for being able to determine P( 70 ≤ Y ≤ 73) are _____ and _____

The P( 70 ≤ Y ≤ 73) is _____

3. The value of z for being able to determine P(Y ≥ 72) is _____

The P(Y ≥ 72) is _____

4. The closest value of z for being able to determine the value of y such that 10% of the values Y are less

than that y is ______

                The approximate value of y such that 10% of the values Y are less than that y is ______

For each part of this question, complete the statement or statements by typing in your answers in the provided spaces:

1. If the probabilities: that event A occurs is .55; that event B occurs is .60; and, that both A and B occur is .35,

The probability (up to 4 decimal places if needed) that events A or B (or both) occur is ______

The probability (up to 4 decimal places if needed) that event B occurs given that A occurs is ______          

2. If the probabilities: that event A occurs is .40; that event B occurs is .7; and, that event B occurs given that event A occurred is .4,

Complete the following contingency table by typing the appropriate probabilities (to 2-decimal places in the spaces provided

                                                      A                   A^C              total

                                    B           ____           ____           ____                     

                                    B^C         ____            ____            ____

                              Total        ____           ____            ____

c. Given the following probability distribution of X:

x                P(x)

0                .15

1                .20

2                .40

3                .25

                  The expected value (to 2-decimal places) of X is _____

                  If Y = 3 + 4X, the expected value (to 2 decimal places) of Y is _____

***URGENT*** TEST

1. At one large university, freshmen account for the 40% of the student body, if a group of 15 students is randomly chosen by the school newspaper to comment on textbook prices; what is the probability that at most three of the students are from freshmen? Round your answer to four decimal places (Use Binomial distribution to model this probability)

2.    The Test score in statistics of a class of students has a normal distribution with mean 65 and standard deviation 20. If a student in that class gets

40 marks in statistics, what is the corresponding z-score of the student’s mark. Round your answer to 2 decimal places.

4. Find the following probabilities: (Round your answer to four decimal places)

1. P(Z ≤ -1.5)                   b)   P(Z ≥ 0.25)                 c)   P(- 0.5 ≤ Z   ≤ 0.5) d)   P(Z ≤ -.45   0r Z ≥ 1.15

5. Assume that the distribution of weights of adult males is normal with a mean of 179.8 lbs. and a standard deviation of 45 lbs. Find the probability
    that a randomly selected adult male would have weight less than 170 lbs.   Round your answer to four decimal places.

Voter Turnout. Minnesota had the highest turnout rate of any state for the 2016 presidential election. (United States Election Project website) Political analysts wonder if turnout in rural Minnesota was higher than turnout in the urban areas of the state. A sample shows that 663 of 884 registered voters from rural Minnesota voted in the 2016 presidential election, while 414 out of 575 registered voters from urban Minnesota voted.

1. Formulate the null and alternative hypotheses that can be used to test whether registered voters in rural Minnesota were more likely than registered voters in urban Minnesota to vote in the 2016 presidential election.
2. What is the proportion of sampled registered voters in rural Minnesota that voted in the 2016 presidential election?
3. What is the proportion of sampled registered voters in urban Minnesota that voted in the 2016 presidential election?
4. At α = 0.05, test the political analysts' hypothesis. What is the p-value and what conclusion do you draw from your results?

A business consultant wanted to investigate if providing day care facilities on a company’s premises reduces the absentee rate of parents working for the company. The consultant took a sample of 52 parents not working for companies providing on site daycare. These parents missed an average of 8.2 days of work last year. Another sample of 46 parents working for companies providing on site daycare showed an average 6.5 missed days of work last year. Assume that the standard deviation for the two populations are 1.75 days and 1.3 days respectively.

a) Construct a 94% confidence interval for the difference between the population means. Interpret your confidence interval in the context of the question.

b) Using a 2.5% level of significance, can you conclude that the mean number of days missed per year by parents not working for the companies providing on site daycare is greater than the number of days missed per year by parents working for companies that do provide on site daycare? Conduct a hypoth- esis test and write a conclusion in the context of the question.

If P(-2 < Z < k)=.6 , where Z is a standard normal random variable, then k is... Select one: a. 0.195 b. 0.73 c. 0.55 d. -0.40

How much "statistical significance" do you need to feel confident in regression results? What could potentially affect those results and make them misleading, i.e., appear to be stronger than they are? Explain, discuss.

Complete the following statements by typing your answers in the spaces provided.  If you are asked to determine the probabilities, state your answers to 4 decimal places.  If you are asked to determine a value of Y, state your answers to 2 or 3 decimal places.  Because you will be typing in your answers,  I cannot ask you to draw diagrams as I have done in my previously posted practice finals and solutions to examples, I suggest when you are working on your answers on scrap pieces of paper (or a print out of the exam sheets), draw the diagrams.  You are more likely to get the right answer if you use diagrams.  For each of these statements I am asking you fill in more than one blank so that I can give you part marks if your intermediate calculation is correct but your final calculation is wrong.   

When answering each of the following, the random variable Y is normally distributed with a mean of 65 and a standard deviation of 4.

1. The value of z for being able to determine P(Y ≤ 60) is _____

The P(Y ≤ 60) is _____

2. The 2 values of z for being able to determine P( 70 ≤ Y ≤ 73) are _____ and _____

The P( 70 ≤ Y ≤ 73) is _____

3. The value of z for being able to determine P(Y ≥ 72) is _____

The P(Y ≥ 72) is _____

4. The closest value of z for being able to determine the value of y such that 10% of the values Y are less

than that y is ______

                  The approximate value of y such that 10% of the values Y are less than that y is ______

Complete the following statements by typing your answers in the spaces provided.  If you are asked to determine the probabilities, state your answers to 4 decimal places.  If you are asked to determine a value of Z, state your answers to 2 or 3 decimal places.  Because you will be typing in your answers,  I cannot ask you to draw diagrams as I have done in my previously posted practice finals and solutions to examples, I suggest when you are working on your answers on scrap pieces of paper (or a print out of the exam sheets), draw the diagrams.  You are more likely to get the right answer if you use diagrams.  

1. The P(Z ≤ - 1.74) is _____

2. The P(Z ≥ 0.64) is _____

3. The P(1.24 ≤ Z ≤ 2.72) is _____

4. The value of z such that P(Z ≤ z) = .2061 is _____

5. The value of z such that P(Z ≥ z) = .3050 is _____

6. The value of z such that P(- z ≤ Z ≤ z) = .7960 is _____

7. The value of z that is exceeded 10% of the time is _____

Exercise 9-56

A shopping centre wants to examine the amount of space required for parking. Studies indicated that 68% of staff and shoppers use public transportation. A survey of 1,002 was taken, and 663 responded that they used public transportation.

a. State the null hypothesis and the alternate hypothesis. Round the final answers to 2 decimal places.

H₀: p =           

H₁: p ≠           

b. State the decision rule for 0.10 significance level. (Negative answer should be indicated by a minus sign. Round the final answers to 2 decimal places.)

Reject H₀ if z > or z < .

c. Compute the value of the test statistic. (Negative answer should be indicated by a minus sign. Round the final answer to 2 decimal places.)

Value of the test statistic           

d. At the 0.10 significance level, is it reasonable to conclude that the survey results indicate a change?

H₀. There is evidence to indicate that the results have changed.

An experiment was performed to compare the fracture toughness of high-purity 18 Ni maraging steel with commercial-purity steel of the same type. For m = 34 specimens, the sample average toughness was x = 63.4 for the high-purity steel, whereas for n = 37 specimens of commercial steel y = 57.8. Because the high-purity steel is more expensive, its use for a certain application can be justified only if its fracture toughness exceeds that of commercial-purity steel by more than 5. Suppose that both toughness distributions are normal.

(a) Assuming that σ₁ = 1.2 and σ₂ = 1.1, test the relevant hypotheses using α = 0.001. (Use μ₁ − μ₂, where μ₁ is the average toughness for high-purity steel and μ₂ is the average toughness for commercial steel.)
Calculate the test statistic and determine the P-value. (Round your test statistic to two decimal places and your P-value to four decimal places.)

(b) Compute β for the test conducted in part (a) when μ₁ − μ₂ = 6. (Round your answer to four decimal places.)
β =

You may need to use the appropriate table in the Appendix of Tables to answer this question.