Income

A. The mean or average of the ranked above data for a village in Peru is:

a. $245.44

b. $345.44

c. $123.44

d. $200.56

B. Suppose that the covariance between the ranked income and the cumulative distribution of income is 33.24. The Gini coefficient for this village is approximately:

a. .212
b. .223

c. .271

d. .281

he final exam grade of a statistics class has a skewed distribution with mean of 78 and standard deviation of 7.8. If a random sample of 30 students selected from this class, then what is the probability that average final exam grade of this sample is between 75 and 80?

Part 1

A company produces steel rods. The lengths of the steel rods are normally distributed with a mean of 198.9-cm and a standard deviation of 2.3-cm. For shipment, 22 steel rods are bundled together.

Find P₅₂, which is the average length separating the smallest 52% bundles from the largest 48% bundles.
P₅₂ = _____ cm

Part 2

Scores for a common standardized college aptitude test are normally distributed with a mean of 513 and a standard deviation of 96. Randomly selected men are given a Test Prepartion Course before taking this test. Assume, for sake of argument, that the test has no effect.

If 1 of the men is randomly selected, find the probability that his score is at least 616.
P(X > 616) = __________

If 5 of the men are randomly selected, find the probability that their mean score is at least 616.
P(M > 616) = __________

Part 3

A population of values has a normal distribution with μ=152.8 and σ=59.7. You intend to draw a random sample of size n=211.

Find the probability that a single randomly selected value is between 140.9 and 164.3.
P(140.9 < X < 164.3) = __________

Find the probability that a sample of size n=211 is randomly selected with a mean between 140.9 and 164.3.
P(140.9 < M < 164.3) = _____________

Part 4

A population of values has a normal distribution with μ=164.8 and σ=37.2. You intend to draw a random sample of size n=108.

Find the probability that a sample of size n=108 is randomly selected with a mean between 154.1 and 169.8.
P(154.1 < M < 169.8) = _________

Part 5

A population of values has a normal distribution with μ=143.9 and σ=89.6. You intend to draw a random sample of size n=217.

Find the probability that a single randomly selected value is between 133 and 162.1.
P(133 < X < 162.1) = ________

Find the probability that a sample of size n=217 is randomly selected with a mean between 133 and 162.1.
P(133 < M < 162.1) = _______________

Part 6

A population of values has a normal distribution with μ=179 and σ=98.2. You intend to draw a random sample of size n=75.

Find the probability that a sample of size n=75 is randomly selected with a mean less than 181.3.
P(M < 181.3) = ___________

Twelve dogs from three different breeds (basenji, Shetland sheepdog, beagle) were either indulged or disciplined between the third and eight weeks of their lives. The indulged animals were encouraged in play, aggression, and climbing on their caretaker. In contrast, the disciplined dogs were retrained to their handler’s lap, taught to sit, stay, come, and so on. The indulged-disciplined treatment was inspired by reports that overindulged children cannot often inhibit their impulses in structured situations. Each dog was taken into a room with a bowl of meat. The dog was hungry but the handler prevented it from eating for 3 minutes by hitting on the rump with a newspaper and shouting ‘no’. The handler left the room and the length of time it took the dog to begin eating the meat was recorded. Presumably, the indulged dog should go to the food more quickly than the disciplined dogs.

a. State the hypotheses for each of the three separate tests included in the two-factor ANOVA.

b. Use SPSS or manual calculation to test the significance of main and the interaction effects.

c. Present the effect size for each of the three tests

Determine whether the value is a discrete random​ variable, continuous random​ variable, or not a random variable.

a. The number of bald eagles in a countrynumber of bald eagles in a country

b. The number of points scored during a basketball gamenumber of points scored during a basketball game

c. The response to the survey question "Did you smoke in the last week question mark "response to the survey question "Did you smoke in the last week?"

d. The number of free dash throw attempts before the first shot is madenumber of free-throw attempts before the first shot is made

e. The square footage of a housesquare footage of a house

f. The height of a randomly selected giraffeheight of a randomly selected giraffe

a. Is the

number of bald eagles in a countrynumber of bald eagles in a country

a discrete random​ variable, a continuous random​ variable, or not a random​ variable?

A.

It is a

continuouscontinuous

random variable.

B.

It is a

discretediscrete

random variable.

C.

It is not a random variable.

b. Is the

number of points scored during a basketball gamenumber of points scored during a basketball game

a discrete random​ variable, a continuous random​variable, or not a random​ variable?

A.

It is a

continuouscontinuous

random variable.

B.

It is a

discretediscrete

random variable.

C.

It is not a random variable

c. Is the

response to the survey question "Did you smoke in the last week question mark "response to the survey question "Did you smoke in the last week?"

a discrete random​ variable, a continuous random​ variable, or not a random​ variable?

A.

It is a continuous random variable.

B.

It is a discrete random variable.

C.

It is not a random variable.

d. Is the

number of free dash throw attempts before the first shot is madenumber of free-throw attempts before the first shot is made

a discrete random​ variable, a continuous random​ variable, or not a random​ variable?

A.

It is a

discretediscrete

random variable.

B.

It is a

continuouscontinuous

random variable.

C.

It is not a random variable.

e. Is the

square footage of a housesquare footage of a house

a discrete random​ variable, a continuous random​ variable, or not a random​variable?

A.

It is a

continuouscontinuous

random variable.

B.

It is a

discretediscrete

random variable.

C.

It is not a random variable.

f. Is the

height of a randomly selected giraffeheight of a randomly selected giraffe

a discrete random​ variable, a continuous random​ variable, or not a random​ variable?

A.

It is a

continuouscontinuous

random variable.

B.

It is a

discretediscrete

random variable.

C.

It is not a random variable.

The following bivariate data set contains an outlier.

What is the correlation coefficient with the outlier?
r_w =  (Round to three decimal places)

What is the correlation coefficient without the outlier?
r_wo =  (Round to three decimal places)

8.29 In a survey of 1,003 adults concerning complaints about restaurants, 732 complained about dirty or ill-equipped bathrooms and 381 complained about loud or distracting diners at other tables.

a. Construct a 95% confidence interval estimate for the population proportion of adults who complained about dirty or ill-equipped bathrooms )

b. Construct a 95% confidence interval estimate for the population proportion of adults who complained about loud or distracting diners at other tables.

c. How would the manager of a chain of restaurants use the results of (a) and (b)?

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 _____   %