Directions: Read each item carefully answers clearly in the space provided.You should also show your work on this exam in the space provided. Values taken from tables should be reported as it is.Final results from computations should be rounded off to two decimal places where appropriate.

1.The following are a list of variables that will almost certainly vary across students in a large undergraduate introductory statistics course.

(a)Favorite beverage

(b)Year of birth

(c)Typing speed

(d)Handedness (e.g., left or right handed)

(e)Age

(f)Occupation

(g)Self-report of Assertiveness

For questions 1a to 1d that follow choose the variable or variables that best represent the level of measurement.

a) Which variables would typically be measured on a nominal scale of measurement? (1.5p)

b) Which variable would likely be measured on an interval, but not a ratio scale? (.5p)

-(F) Occupation

c) Which two variables are most likely to be measured on a ratio scale? (1p)

d) As typically measured, which variable represents at least an ordinal scale of measurement, but probably not a true interval scale? (.5p)

2.An investigation of wages paid to its employees by a large company was undertaken as a result of an allegation of discrimination. Data was collected for 1000 randomly selected employees. The data included employee ID, gender, race, annual wages in dollars (Salary), whether the employee had full-time status or part-time status (Full_Part), number of years of education (Ed), and number of years with the company (Tenure). The first two rows of data in the worksheet are displayed below.

a.How many cases does this data set contain? (1.5p)

b.How many variables does this data set contain? (1p)

c.How many quantitative variables does this data set contain, and what are they? (1p)

d.How many qualitative variables does this data set contain, and what are they? (1p)

3.A sample was taken of the salaries of 10 employees of a large company. The following are the salaries (in thousands of dollars) for this year. For convenience, the data are ordered.

28

34

41

42

45

45

52

61

72

77

a)The median salary of the 10 employees is: (1p)

b)Suppose each employee in the company receives a $3000 raise for next year (each employee's salary is increased by $3000). The mean salary for the employees will: (1 p)

c)Suppose each employee in the company receives a $3000 raise for next year (each employee's salary is increased by $3000). The median salary for the employees working for the company will: (1 p)

d)Suppose each employee in the company receives a $3000 raise for next year (each employee's salary is increased by $3000). The standard deviation of the salaries for the employees will: (1p)

EXCEL must be used for question #4. Hand calculation using formulas are not accepted for this question. Do not forget to include the Boxplot for question 4-g. Results from computations should be rounded off to two decimal places where appropriate.

4.An entrepreneur faces many bureaucratic and legal hurdles when starting a new business. The World Bank collects information about starting businesses throughout the world. It has determined the time, in days, to finish the procedures required to start a business.17 Data for 187 countries are included in the data set, TTS. For this section, we examine data, rounded to integers, for a sample of 24 of these countries. Here are the data:

a)Find the mean time to start a business for 24 countries in our data set: (1p)

b)Find the median time to start a business for 24 countries in our data set: (1p)

c)Which measure do you prefer for describing the center of this distribution? Explain your answer. (2p)

d)Compute the quartiles (Q1, Q2, Q3), and find the IQR for these data. Are there outliers in the time to start a business data set? If so, identify and name any outliers. (3p)

e)Compute the standard deviation of time to start a business for 24 countries in the data set: (1p)

f)Which measure do you prefer for describing the spread of this distribution? Explain your answer. (1p)

g)Make a boxplot for these data and explain & describe the distribution using only the information in the boxplot. (3p)

Standard normal table (z score table) must be used for question #5 along with formulas. Show your work and computation for each question to be able to receive the full credit. Values taken from tables should be reported as it is.Final results from computations should be rounded off to two decimal places where appropriate.

5.A life satisfaction Test has a population mean of = 500 and a population standard deviation of =100. Suppose you randomly select a sample of 80 participants and administer the Life Satisfaction Test to each participant.

a.What would you expect the mean of this sample to be ()? (1p)

b.What is the standard error of the mean for samples of size 80 from this population (_x)? (1p)

c.What is the probability that this sample will be one of the samples that will have a mean Life Satisfaction score greater than 520? P( > 520) =? (3p)

d.What is the probability that this sample will be one of the samples that will have a mean Life Satisfaction score between 490 and 510? P(490 < <510) =? (4p)

6.Consider the following probability histogram for a random variable X.

X axis shows the values of random variable X.

Y axis shows the probabilities of random variable X.

Create the probability distributions of a random variable X approximately using the values on the histogram. (3p)

7.From the probability distribution, find the mean for the random variable x, which represents the number of cars per household in a town of 1000 households. (2p)

x

0

1

2

3

P(x)

0.5

0.3

0.05

0.02

8.A survey of U.S. adults ages 18 and older asked about their use of social media. One analysis examined the relationship between Facebook usage and age. Here are the data:

For the survey respondents:

a)What is the probability that a randomly chosen respondent is a Facebook user? (2p)

b)What is the conditional probability a randomly chosen respondent is a Facebook user, given the person's age is between 30 and 49 years? (3p)

c)What is the conditional probability a randomly chosen respondent is between 30 and 49 years old, given that the person is a Facebook user? (3p)

9.A university claims that at least 80% of its basketball players get degrees. An investigation examines the fate of 20 players who entered the program over a period of several years that ended six years ago. Of these players, 11 graduated and the remaining nine are no longer in school. If the university's claim is true, the number of players who graduate among the 20 should have the binomial distribution with and at least equal to 0.8.

a)Find the mean number of graduates out of 20 players if 80% of players graduate. (2p)

b)Find the standard deviation of the count X if 80% of players graduate. (2p)

c)Suppose now that the 20 players came from a population of which p = 0.9 graduated. What is the standard deviation of the count of graduates? If p = 0.99, what is ? What does your work show about the behavior of the standard deviation of a binomial distribution as the probability p of success gets closer to 1? (4p)

You could use either EXCEL or formulas for question #10. If you would prefer to use hand calculation, please do not forget to show your work below each question. Values taken from tables should be reported as it is.Final results from computations should be rounded off to two decimal places where appropriate.

10.Average starting salary.The University of Texas at Austin McCombs School of Business performs and reports an annual survey of starting salaries for recent bachelor's in business administration graduates. For 2017, there were a total of 598 respondents.

1. Respondents who were finance majors were 41.42% of the total responses. Rounding to the nearest integer, what is n for the finance major sample? (3p)

1. For the sample of finance majors, the average salary is $68,145 with a standard deviation of $13,489. What is the 90% confidence interval for average starting salaries for finance majors? (3p)