The following probability distributions of job satisfaction scores for a sample of information systems (IS) senior executives and middle managers range from a low of 1 (very dissatisfied) to a high of 5 (very satisfied).

(a)

What is the expected value of the job satisfaction score for senior executives?

(b)

What is the expected value of the job satisfaction score for middle managers?

(c)

Compute the variance of job satisfaction scores for executives and middle managers.

executivesmiddle managers

(d)

Compute the standard deviation of job satisfaction scores for both probability distributions. (Round your answers to two decimal places.)

executivesmiddle managers

(e)

Compare the overall job satisfaction of senior executives and middle managers.

The average score for senior executives is (lower than? higher than? equal to?) the middle managers score. The standard deviation for senior executives is (lower than, higher than, equal to) the middle managers standard deviation.

Suppose you have selected a random sample of ?=13 measurements from a normal distribution. Compare the standard normal z values with the corresponding t values if you were forming the following confidence intervals.

a)    80% confidence interval
?=
?=

(b)    90% confidence interval
?=
?=

(c)    99% confidence interval
?=
?=

If a dependent variable is binary, is it optimal to use linear regression or logistic regression? Explain your answer and include the theoretical and practical concerns associated with each regression model. Provide a business-related example to illustrate your ideas.

Total plasma volume is important in determining the required plasma component in blood replacement therapy for a person undergoing surgery. Plasma volume is influenced by the overall health and physical activity of an individual. Suppose that a random sample of 46 male firefighters are tested and that they have a plasma volume sample mean of x = 37.5 ml/kg (milliliters plasma per kilogram body weight). Assume that σ = 7.00 ml/kg for the distribution of blood plasma.

(a) Find a 99% confidence interval for the population mean blood plasma volume in male firefighters. What is the margin of error? (Round your answers to two decimal places.)

lower limit =

upper limit =

margin of error =

(b) What conditions are necessary for your calculations? (Select all that apply.)

the distribution of weights is normal

the distribution of weights is uniform

σ is known

σ is unknown

n is large

(c) Find the sample size necessary for a 99% confidence level with maximal margin of error E = 2.00 for the mean plasma volume in male firefighters. (Round up to the nearest whole number.)

____ male firefighters

A market researcher is interested in determining whether the age of listeners influences their preferred musical styles. The following is a contingency table from a random sample of 385 individuals:

AGE

Style_1

Style_2

Style_3

18–25

125

13

6

26–35

87

12

6

36–45

50

22

12

46+

12

25

15

A) what are the numerator degrees of freedom

B) what are the denominator degrees of freedom.

C) Calculate the value of the test statistic – Chi-Square.

D) Using the 95% level of confidence, are these two variables independent?

10. Suppose that X, Y and Z are normally distributed where X ≈ N(100,100), Y ≈ N(400, 400) and

Z ≈ N(64,64). Let W = X + Y + Z.

a) Describe the distribution of W, give a name and parameters E(W) and Var(W).

b) Use Excel or R to generate 200 random values for X, Y and Z. Add these to obtain 200 values for W. Create a histogram for W. In Excel use the NORMINV(rand(),mean, sd) function.

c) Estimate E(W) and Var(W) using the random numbers.

An Illinois state program evaluator is tasked with studying the intelligence of soon-to-graduate high school students in a number of Chicago-area high schools.

One of the specific questions that needs to be answered is, “How do the students of Collins High School, one of Chicago’s lowest-rated high schools in terms of academic achievement, fare in intelligence compared to students of Lincoln Park High School, one of Chicago’s highest-rated high schools in terms of academic achievement?”.

To conduct this study, the program evaluator administers the Wechsler Adult Intelligence Scale, 4th Edition (WAIS-IV) to one 12th grade class from each high school in the Chicago area (if you are interested in learning more about the WAIS-IV, click here).

The following table shows the WAIS-IV scores for student from Collins HS and Lincoln Park HS (note: data were fabricated for purposes of this excersize):

First, complete the below grouped frequency table of WAIS-IV scores for each HS:

Compute the appropriate calculations to complete the following table :

What is the shape of the distribution of intelligence scores (normal, negatively skewed, positively skewed) for Collins HS? Explain how you arrived at your answer.

What is the shape of the distribution of intelligence scores (normal, negatively skewed, positively skewed) for Lincoln Park HS? Explain how you arrived at your answer.

A random sample of 1600 workers in a particular city found 688 workers who had full health insurance coverage. Find a 95% confidence interval for the true percent of workers in this city who have full health insurance coverage. Express your results to the nearest hundredth of a percent.

Answer: _____ to _____   %

Question 3:

In “Orthogonal Design for Process Optimization and Its Application to Plasma Etching”, an experiment is described to determine the effect of flow rate on the uniformity of the etch on a silicon wafer used in integrated circuit manufacturing. Three flow rates are used in the experiment, and the resulting uniformity (in percent) for six replicates is shown below.

1. Does flow rate affect etch uniformity? Use α = 0.05.
2. Do the residuals indicate any problems with the underlying assumptions?
3. Use the Kruskal-Wallis procedure with α = 0.05 to test for differences between mean uniformity at the three different flow rates.

"Black Friday" is the day after Thanksgiving and the traditional first day of the Christmas shopping season. Suppose a recent poll suggested that 66% of Black Friday shoppers are actually buying for themselves. A random sample of 130 Black Friday shoppers is obtained. Answer each problem using the normal approximation to the binomial distribution.

(a)

Find the approximate probability that fewer than 73 Black Friday shoppers are buying for themselves. (Round your answer to four decimal places.)

(b)

Find the approximate probability that between 74 and 84 (inclusive) Black Friday shoppers are buying for themselves. (Round your answer to four decimal places.)

We throw a die independently four times and let X denote the minimal value rolled. (a) What is the probability that X ≥ 4. (b) Compute the PMF of X. (c) Determine the mean and variance of X.

5.
a. Analyze the Bread variable in the SandwichAnts dataset using aov() in R and
interpret your results.
The data may be found here:
install.packages("Lock5Data")
library(Lock5Data)
data(SandwichAnts,package="Lock5Data")
attach(SandwichAnts)
b. State the linear model for this problem. Define all notation and model terms.
c. Create the design matrix for this problem.
d. Estimate model parameters for this problem using ? = (?^T?)^-1?^T?
e. Interpret the meaning of the estimates from part d.
f. Rerun this problem using lm()in R. Interpret the coefficients in the output.
g. Rewrite the model in as a linear regression using dummy variables. Confirm the
results from part f. agree with the results from part g.
h. Perform a one-way ANOVA of Bread using a randomization test on the
SandwichAnts dataset.

Two successive flips of a fair coin is called a trial. 100 trials are run with

a particular coin; on 22 of the trials, the coin comes up “heads” both

times; on 60 of the trials the coin comes up once a “head” and once a

“tail”; and on the remaining trials, it comes up “tails” for both flips. Is this

sufficient evidence ( = : 05) to reject the notion that the coin (and the

flipping process) is a fair one?

(Hint: chi sq)

Find the indicated probabilities using the geometric​ distribution, the Poisson​ distribution, or the binomial distribution. Then determine if the events are unusual. If​ convenient, use the appropriate probability table or technology to find the probabilities.

The mean number of oil tankers at a port city is

1313

per day. The port has facilities to handle up to

1717

oil tankers in a day. Find the probability that on a given​ day, (a)

thirteenthirteen

oil tankers will​ arrive, (b) at most three oil tankers will​ arrive, and​ (c) too many oil tankers will arrive.