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1. Classify the following...

1. Classify the following studies as descriptive or inferential and explain your reasons:

a. (1 pts.) A study on stress concluded that more than half of all Americans older than 18 have at least “moderate” stress in their lives. The study was based on responses of 34,000 households to the 1985 National Health Interview Survey.

b. (1 pts.) A report in a farming magazine indicates that more than 95% of the 400 largest farms in the nation are still considered family operations.

2. Thirty-five fourth-grade students were asked the traditional question “what do you want to be when you grow up? The responses are summarized in the following table:

Employment Frequency Relative Frequency

Teacher 8 0.229

Doctor 6 0.171

Scientist 3 0.086

Police Officer 9 0.257

Athlete 9 0.257

a. (2 pts.) Construct a pie chart for relative frequency

b. (2 pts.) Construct a bar graph for the relative frequencies

3. In a college freshman English course, the following 20 grades were recorded

48 88 47 39 45 44 98 76 84 54

67 91 84 38 75 38 35 82 42 82

Find the:

a. (1 pt.)Quartiles for the above data set

b. (1 pt.)Range for the above data set

c. (1 pt.)Mean for the above data set

d. (1 pt.)Variance for the above data set

4. The age distribution of students at a community college is given below:

Age in Years Number of Students (f)

Under 21 4946

21 - 25 4808

26 - 30 2673

31 - 35 29036

Over 35 525

Suppose a student is selected at random. Let

A = the event the student is under 21

B = the event the student’s age is between 21 and 25

C = the event the student’s age is between 26 and 30

D = the event the student’s age is between 31 and 35

E = the event the student’s age is 35 and under

a. (2 pts.) Find P (B)

b. (2 pts.) Find P (E)

5. A study of the effect of college education on job satisfaction was conducted. A contingency table is presented below:

Attended College Did not Attend Total

Satisfied with job 325 186 511

Not satisfied with job 190 369 559

Total(NNN) NNN-NNNN

If you were to randomly sample an individual from this population, find the probability of selecting an individual who is

a. (2 pts.) satisfied with job

b. (3 pts.) did not attend college given not satisfied with the job

c. (3 pts.) not satisfied with job, and did not attend college

6. The random variable x is the number of houses sold by a realtor in a single month at the real-estate office. Its probability distribution is:

Houses sold (x) Probability P(x)

0 0.09

1 0.24

2 0.21

3 0.17

4 0.03

5 0.15

6 0.09

7 0.02

a. (3 pts.) Compute the mean of the random variable.

b. (3 pts.) Compute the standard deviation of the random variable.

7. According to the U.S. National Center for Health Statistics, the mean height of 18 -24 year old American males is = 69.7 inches. Assume the heights are normally distributed with a standard deviation of 2.7 inches.

Fill in the following blanks:

a. (1 pt.) About 68.26% of 18 -24 year old American males are between ______ and ______ inches tall.

b. (1pt.) About 95.44% of 18 -24 year old American males are between ______ and ______ inches tall.

c. (1 pt.) About 99.74% of 18 -24 year old American males are between ______ and ______ inches tall.

8. The average of freshman college students is = 18.5 years, with a standard

deviation = 0.4 years.

a. (4 pts.) Let x̅ denote the mean age of a random sample of n = 50 students. Determine the mean and standard deviation of the random variable x̅.

b. (4 pts.) Repeat part (a) with n = 100.

9. A brand of salsa comes in jars marked net weight 680 grams. Suppose the actual mean net weight μ = 680 grams with a standard deviation of 22.7 grams. Further suppose that the net weights are normally distributed.

a. (4 pts.) Determine the probability that a randomly selected jar of this brand of salsa will have a weight less than 660 grams.

b. (4 pts.) Determine the probability that the 15 randomly selected jars of this brand of salsa will have a mean weight of less than 660 grams.

(8 pts.) 10. Each year a large university collects data on average beginning monthly salaries of its business school graduates. A random sample of 125 recent graduates with bachelor’s degrees in marketing has a mean stating monthly salary of x̅ = $1635 with a standard deviation of s = $288. Use these data to obtain a 90% confidence interval estimate for the mean starting monthly salary, µ, of all recent graduates with bachelor’s degrees in marketing from this university.

11. A college administrator wants to study the average age of students who drop out of college after only attending one semester. He randomly selects 25 students who are in this group. Their ages are listed below:

35.6 20.1 18.1 21.3 20.1 19.2 18.5 18.9 18.6 18.4 19.2

18.8 17.7 21.0 19.3 24.2 19.0 19.6 18.6 19.4 20.3 20.4

19.6 19.9 19.2

Assume that the ages are normally distributed with a standard deviation of sigma = 0.8 year.

a. (5 pts.) Find

a. (1 pts.) A study on stress concluded that more than half of all Americans older than 18 have at least “moderate” stress in their lives. The study was based on responses of 34,000 households to the 1985 National Health Interview Survey.

b. (1 pts.) A report in a farming magazine indicates that more than 95% of the 400 largest farms in the nation are still considered family operations.

2. Thirty-five fourth-grade students were asked the traditional question “what do you want to be when you grow up? The responses are summarized in the following table:

Employment Frequency Relative Frequency

Teacher 8 0.229

Doctor 6 0.171

Scientist 3 0.086

Police Officer 9 0.257

Athlete 9 0.257

a. (2 pts.) Construct a pie chart for relative frequency

b. (2 pts.) Construct a bar graph for the relative frequencies

3. In a college freshman English course, the following 20 grades were recorded

48 88 47 39 45 44 98 76 84 54

67 91 84 38 75 38 35 82 42 82

Find the:

a. (1 pt.)Quartiles for the above data set

b. (1 pt.)Range for the above data set

c. (1 pt.)Mean for the above data set

d. (1 pt.)Variance for the above data set

4. The age distribution of students at a community college is given below:

Age in Years Number of Students (f)

Under 21 4946

21 - 25 4808

26 - 30 2673

31 - 35 29036

Over 35 525

Suppose a student is selected at random. Let

A = the event the student is under 21

B = the event the student’s age is between 21 and 25

C = the event the student’s age is between 26 and 30

D = the event the student’s age is between 31 and 35

E = the event the student’s age is 35 and under

a. (2 pts.) Find P (B)

b. (2 pts.) Find P (E)

5. A study of the effect of college education on job satisfaction was conducted. A contingency table is presented below:

Attended College Did not Attend Total

Satisfied with job 325 186 511

Not satisfied with job 190 369 559

Total(NNN) NNN-NNNN

If you were to randomly sample an individual from this population, find the probability of selecting an individual who is

a. (2 pts.) satisfied with job

b. (3 pts.) did not attend college given not satisfied with the job

c. (3 pts.) not satisfied with job, and did not attend college

6. The random variable x is the number of houses sold by a realtor in a single month at the real-estate office. Its probability distribution is:

Houses sold (x) Probability P(x)

0 0.09

1 0.24

2 0.21

3 0.17

4 0.03

5 0.15

6 0.09

7 0.02

a. (3 pts.) Compute the mean of the random variable.

b. (3 pts.) Compute the standard deviation of the random variable.

7. According to the U.S. National Center for Health Statistics, the mean height of 18 -24 year old American males is = 69.7 inches. Assume the heights are normally distributed with a standard deviation of 2.7 inches.

Fill in the following blanks:

a. (1 pt.) About 68.26% of 18 -24 year old American males are between ______ and ______ inches tall.

b. (1pt.) About 95.44% of 18 -24 year old American males are between ______ and ______ inches tall.

c. (1 pt.) About 99.74% of 18 -24 year old American males are between ______ and ______ inches tall.

8. The average of freshman college students is = 18.5 years, with a standard

deviation = 0.4 years.

a. (4 pts.) Let x̅ denote the mean age of a random sample of n = 50 students. Determine the mean and standard deviation of the random variable x̅.

b. (4 pts.) Repeat part (a) with n = 100.

9. A brand of salsa comes in jars marked net weight 680 grams. Suppose the actual mean net weight μ = 680 grams with a standard deviation of 22.7 grams. Further suppose that the net weights are normally distributed.

a. (4 pts.) Determine the probability that a randomly selected jar of this brand of salsa will have a weight less than 660 grams.

b. (4 pts.) Determine the probability that the 15 randomly selected jars of this brand of salsa will have a mean weight of less than 660 grams.

(8 pts.) 10. Each year a large university collects data on average beginning monthly salaries of its business school graduates. A random sample of 125 recent graduates with bachelor’s degrees in marketing has a mean stating monthly salary of x̅ = $1635 with a standard deviation of s = $288. Use these data to obtain a 90% confidence interval estimate for the mean starting monthly salary, µ, of all recent graduates with bachelor’s degrees in marketing from this university.

11. A college administrator wants to study the average age of students who drop out of college after only attending one semester. He randomly selects 25 students who are in this group. Their ages are listed below:

35.6 20.1 18.1 21.3 20.1 19.2 18.5 18.9 18.6 18.4 19.2

18.8 17.7 21.0 19.3 24.2 19.0 19.6 18.6 19.4 20.3 20.4

19.6 19.9 19.2

Assume that the ages are normally distributed with a standard deviation of sigma = 0.8 year.

a. (5 pts.) Find

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