3. (i) In a random selected students in Mandalay University, while asking about his/her faculty, the following table was obtained.

(a) What is this table called? What are their positive relationship between sex and major?

(b) How many observations are there for this study?

(c) How many female students are there for this study?

(d) How many variables are there for this study? Identify these variables.

(e) Are these variables qualitative or quantitative? Explain your answer.

(f) If these variables are qualitative, are they nominal or ordinal?

(g) What analysis do you apply when you want to study the relationship between gender and faculty?

1. (i) How do you understand the four levels of measurement and give your own example?

(ii) A company’s human resources department recently selected a sample of fifteen people. They compared the employees’ performance rating (based on a 100-point scale) and the number of overtime hours the employees had worked in the past six months. The following SPSS output were recorded.

                                    Correlation

(a) What is the sample size for this problem?

(b) What is the value of correlation coefficient?

(c) Describe two variables that might exhibit such relationship? Explain your reasoning.

(d) Write down the null and alternative hypotheses.

(e) Which level is significant for this problem?

(f) State a conclusion for your test.

Minimum spanning trees were initially design to solve electrical grid problems but now have many more applications such as computer networks, transportation networks, and supply networks. Describe a business problem where minimum spanning trees can be used to find a solution.

Describe this relationship shown in the table

What two things happen to your sampling distribution as you increase sample size? . Suppose you have a normally distributed population. You decide to collect 10 samples from this population and your colleague collects 30 samples from this population. a. Hand draw the original population, your sampling distribution, and your colleague’s sampling distribution. b. What changes as you increase the sample size?

A manufacturing company prepares a box of 25 items for shipment, and a random sample of 3
items is selected and tested for defectives. If any defectives are found, the entire box is sent
back for 100% screening; if no defectives are found, the box is shipped.

What is the distribution of the number of defective items found in the random
sample? (I think it is NegBin)

What is the probability that a box containing 3 defectives will be shipped?

What is the probability that a box containing 1 defective will be sent back for
screening?

A research is interested in whether the mean score on a particular aptitude test for students who attend rural elementary schools is higher than the score of elementary school students in general (ux=50), ox=10). She tests a random sample of 28 rural elementary school students and finds the sample mean to be 56.

Using alpha=.05, conduct the 8 steps hypothesis testing to determine whether the rural elementary school students have a significantly higher aptitude score than elementary students in general.

An employee of a small software company in Minneapolis bikes to work during the summer months. He can travel to work using one of three routes and wonders whether the average commute times (in minutes) differ between the three routes. He obtains the following data after traveling each route for one week.

Route 1 34 35 29 36 29

Route 2 21 28 25 30 24

Route 3 22 27 25 30 26

a-1. Construct an ANOVA table.

a-2. At the 1% significance level, do the average commute times differ significantly between the three routes. Assume that commute times are normally distributed.

b. Use Tukey’s HSD method at the 1% significance level to determine which routes' average times differ.

A consultant was hired to build an optimization model for a large marketing research company. The model is based on a consumer survey that was taken in which each person was asked to rank 30 new products in descending order based on their likelihood of purchasing the product. The consultant was assigned the task of building a model that selects the minimum number of products (which would then be introduced into the marketplace) such that the first, second, and third choice of every subject in the survey is included in the list of selected products. While building a model to figure out which products to introduce, the consultant’s boss walked up to her and said: “Look, if the model tells us we need to introduce more than 15 products, then add a constraint which limits the number of new products to 15 or less. It’s too expensive to introduce more than 15 new products.”

Evaluate this statement in terms of what you have learned so far about constrained optimization models.

In a super fast photonic switch that you are designing, each incoming photon is directed to output port ”A” with probability p, and to output port B with probability 1 − p, independently. Let R be the total number of photons going to port A and let G be the number of items going to port B in a certain amount of time, during which n photons pass through the switch.

(a) Determine the PMF, expected value, and variance of the random variable R.

(b) Evaluate P(A), the probability that the first photon ends up being the only one sent to its port.

(c) Find P(B), the probability that at least one port ends up receiving exactly one photon in this time interval.

(d) Evaluate the expectation and variance for the difference, D = R − G.

(e) Assume n ≥ 2. Given that both of the first two input photons go to port A, find the conditional expectation, variance and PMF of R.

Consider the following data drawn independently from normally distributed populations: (You may find it useful to reference the appropriate table: z table or t table)

a. Construct the 99% confidence interval for the difference between the population means. Assume the population variances are unknown but equal. (Round all intermediate calculations to at least 4 decimal places and final answers to 2 decimal places.)
  

b. Specify the competing hypotheses in order to determine whether or not the population means differ.
  

• H₀: μ₁ − μ₂ = 0; H_A: μ₁ − μ₂ ≠ 0

• H₀: μ₁ − μ₂ ≥ 0; H_A: μ₁ − μ₂ < 0

• H₀: μ₁ − μ₂ ≤ 0; H_A: μ₁ − μ₂ > 0

c. Using the confidence interval from part a, can you reject the null hypothesis?
  

• Yes, since the confidence interval includes the hypothesized value of 0.

• No, since the confidence interval includes the hypothesized value of 0.

• Yes, since the confidence interval does not include the hypothesized value of 0.

• No, since the confidence interval does not include the hypothesized value of 0.

d. Interpret the results at αα = 0.01.

• We conclude that population mean 1 is greater than population mean 2.

• We cannot conclude that population mean 1 is greater than population mean 2.

• We conclude that the population means differ.

• We cannot conclude that the population means differ.

Bank of America's Consumer Spending Survey collected data on annual credit card charges in seven different categories of expenditures: transportation, groceries, dining out, household expenses, home furnishings, apparel, and entertainment. Using data from a sample of 42 credit card accounts, assume that each account was used to identify the annual credit card charges for groceries (population 1) and the annual credit card charges for dining out (population 2). Using the difference data, the sample mean difference was d=$850, and the sample standard deviation was s = $1123.

a. Formulate the null and alternative hypotheses to test for no difference between the population mean credit card charges for groceries and the population mean credit card charges for dining out.

b. Use .05 level of significance. Can you conclude that the population means differ?

What is the p-value? (to 6 decimals)

c. Which category, groceries or dining out, has a higher population mean annual credit card charge? a. Groceries b. dining out

What is the point estimate of the difference between the population means? Round to the nearest whole number. What is the 95% confidence interval estimate of the difference between the population means? Round to the nearest whole number.

Samples of starting annual salaries for individuals entering the public accounting and financial planning professions follow. Annual salaries are shown in thousands of dollars.

(a)

Use a 0.05 level of significance and test the hypothesis that there is no difference between the starting annual salaries of public accountants and financial planners.

State the null and alternative hypotheses.

H₀: The two populations of salaries are not identical.
H_a: The two populations of salaries are identical.H₀: Median salary for public accountants − Median salary for financial planners ≤ 0
H_a: Median salary for public accountants − Median salary for financial planners > 0     H₀: Median salary for public accountants − Median salary for financial planners ≥ 0
H_a: Median salary for public accountants − Median salary for financial planners < 0H₀: The two populations of salaries are identical.
H_a: The two populations of salaries are not identical.H₀: Median salary for public accountants − Median salary for financial planners > 0
H_a: Median salary for public accountants − Median salary for financial planners = 0

Find the value of the test statistic.

W =

Find the p-value. (Round your answer to four decimal places.)

p-value =

What is your conclusion?

Reject H₀. There is not sufficient evidence to conclude that there is a significant difference between the starting annual salaries of public accountants and financial planners.

Reject H₀. There is sufficient evidence to conclude that there is a significant difference between the starting annual salaries of public accountants and financial planners.   

  Do not reject H₀. There is not sufficient evidence to conclude that there is a significant difference between the starting annual salaries of public accountants and financial planners.

Do not reject H₀. There is sufficient evidence to conclude that there is a significant difference between the starting annual salaries of public accountants and financial planners.

(b)

What are the sample median annual salaries (in $) for the two professions?

Public Accountants sample median = $

Financial Planners sample median = $

Suppose a simple random sample of athletes in the NBA heights is taken. There were 28 athletes in the sample with a mean height of 78.4 inches and standard deviation of 2 inches. It has been confirmed through statistical analysis that NBA player heights follows a normal distribution.

a. what parameter are we estimating?

b. Explain the requirements as they relate to the problem

c.What is the point estimate of the parameter?

d.Input the margin of error for a 95% confidence interval for the true average height of NBA players.
Write the equation you used and the numbers .

e. Create and input your interval using your answer in part d.

f.  Interpret your interval. (explanation)

g.Use your interval to respond to the statement that the true average height of NBA players is less than than 78.4. Thoroughly explain why you are responding the way you are.

h. What does the central limit theorem say about the sample distribution of the sample average of basketball player heights for this problem?

please show all work and round to the fourth on all ansers