Statistic test

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DAH Test#1 is due Sunday, JUNE 23, 2019 by midnight.

MAT 102: DAH TEST #1 Form A SUMMER 2019 Prof. DeSanto

1. A sample of underweight babies was fed a special diet and the following weight gains (lbs.) were observed at the end of

three months.

6.7 5.8 3.8 3.6 4.9 4.5 5.2 4.9 4.5

The mean and standard deviation respectively are:

a. 4.88, 0.96 b. 4.7, 1.22 c. 4.15, 3.6 d. 4.87, 0.90 e. 4.70, 1.06

2. When measuring the center of the data in a skewed distribution, the median would be a preferred descriptive statistic

over the mean for most purposes because:

a. the median is the most frequent number while the mean is most likely

b. the median is less than the mean and smaller numbers are always appropriate for the center

c. the mean may be too heavily influenced by outliers and doesn’t give a good indication of the center

d. the mean measures the spread in the data

e. the median measures the arithmetic average of the data excluding outliers

3. The distribution of the student heights at a large college is approximately bell shaped. If the average height is 66

inches, and approximately 68% of the heights fall between 51 and 81 inches, then the standard deviation of the height

distribution is approximately equal to:

a. 5

b. 10

c. 12

d. 15

e. 20

4 - 5. Margaret, an archeologist, is conducting a test to determine if there is a positive linear relationship between the total

height of a dinosaur and its leg length. Her random sample of 10 dinosaur total heights (in feet) and leg lengths (in feet)

produced the results shown in the following TI calculator screen. Use the TI calculations in the following screen shot to help

you answer questions: 4 & 5.

4. What percent of variation in the dinosaur's total height can be accounted for by the variation in the dinosaur's leg length?

a) 17% b) 2.3% c) 52% d) 72% e) none of these

5. What would you predict for a dinosaur's total height given that its leg length is 3.5 feet?

a) 25.23 feet b) 17.18 feet c) 24.56 feet d) 22.99 feet

MAT 102: DAH TEST #1 Form A SUMMER 2019 Prof. DeSanto

6 – 7. An achievement exam was given to a population of 1,000 students. However, only seven of these 1,000 student scores are listed along with their respective z score and percentile rank in the following table.

TEST SCORE 68 72 80 86 88 90 92

z score -3 -2 0 1.5 2 2.5 3

percentile rank 15 25 40 50 70 90 97

6. Using the table information, the mean test score for all the 1,000 students with the appropriate symbol to denote this

result is: a) x = 68 b)  = 86 c) x = 72 d)  = 80 e) x = 88

7. Using the table information, the standard deviation of all the 1,000 students with the appropriate symbol used to denote

this result is: a) σ = 4 b) s = 4 c) σ = 8 d) s = 6 e) σ = 2

8. If the mean test score of a distribution of statistics exam scores is 72 with a standard deviation of 15, then determine the test

score (to the nearest whole number) of a student that had a z score of -1.35?

a) 71 b) 51 c) 67 d) 52 e) cannot be estimated

9. If one set of paired data x and y has an r = 0.74 and a different set of paired data c and d has an r = -0.83, then which set of paired data has the stronger correlation? (assume both sets have the same sample size.)

a) x and y

b) c and d

c) not enough information

10. Suppose a frequency distribution is skewed with a median of $80.00 and a mode of $95.00.

Which of the following is a possible value for the mean of the skewed distribution?

a. $86 b. $91 c. $64 d. $105 e. None of these

11. If a population of college student ages is skewed right, then this indicates:

a. there are more older students within the population b. the median age is greater than the mean age

c. as the age of a student increases, the frequency of the student ages decreases.

d. the modal student age is greater than the median age

e. not enough information

12. If the statistics for family income in a certain community are:

mean = $37,000 median = $25,000 mode = $23,000 range = $15,000 and std deviation = $6,000

then which one of the following statements is NOT correct?

a. most of the families made $23,000 b. $31,000 is one standard deviation below the mean

c. the variance is approximately $77.46 d. the income $25,000 is the second quartile

e. the z score of the income $46,000 is 1.50.

13. According to the latest Gallup Poll, 40% of American Teenagers purchase designer jeans. Assume this result is true for all

teenagers. What is the probability that out of the next 8 teenagers who purchase jeans at most 1 will purchase designer jeans?

a) 0.0168 b) 0.2090 c) 0.0896 d) 0.1239 e) 0.1064

MAT 102: DAH TEST #1 Form A SUMMER 2019 Prof. DeSanto

14. Matthew, who is 25 years old, prefers to date a young lady who is approximately 20 years old. He is considering two computer dating services: Dating Service I and Dating Service II. The statistics of the female ages on file for each dating

service is given in the following table.

statistics on the

female ages

Dating Service I

Dating Service II

mean 20 yrs. 20 yrs.

standard deviation 1.58 yrs. 5.80 yrs.

Matthew has a better chance of dating a girl who is approximately 20 years of age from:

a. Dating Service I b. Dating Service II c. Both the same d. Not enough information

15. The following back to back stem and leaf display shows the number of books read in a year by a random sample of

High School and College Students.

College HS

7 0

3 6 6 1 0 0 3 5

1 2 3 4 2 1 2 4 4 6

6 8 8 9 3 1 8 9

2 8 4 0 1

5

6

3 7

Consider the three statements:

I. Seven College students did not read any books. II. College median is equal to the HS median. III. Mean is greater than the median for both groups. Which of the above statements are true?

a. I only b. II only c. III only d. I and II e. II and III

Use the following frequency table containing randomly selected people’s ages shopping at a local mall to answer

questions 16 and 17.

AGE FREQUENCY

0-4 1

5-9 3

10-14 6

15-19 9

20-24 11

25-29 10

16. What percent of the shoppers were older than 4 but younger than 20?

a. 14

b. 16

c. 35

d. 45

e. 75

17. What is the shape of this distribution of shopper’s ages?

a. skewed right

b. bimodal

c. skewed left

d. bell shaped

e. Uniform

MAT 102: DAH TEST #1 Form A SUMMER 2019 Prof. DeSanto

Questions 18 through 20 refer to the accompanying graph that uses box plots to compare the number of followers that a

person has on Twitter for 4 local colleges. This survey was for college students who had fewer than 300 followers on

Twitter. Pick the choice that best represents the answer.

18. Which college has the largest value for the 75th percentile?

a. Nassau CC b. Suffolk CC c. Hofstra d. Stonybrook

19. Which college would you say has the most consistent data?

a. Nassau CC b. Suffolk CC c. Hofstra d. Stonybrook

20. What is the shape of the Stonybrook data?

a. skewed left b. uniform c. skewed right d. approximate bell curve

Submit this answer sheet with your work!

Name:______________________________________________________________ SUMMER ‘19 Prof. DeSanto

MAT 102: DAH Exam 1 Form A

PART II: Place your answers on the provided answer pages. Be sure to answer all parts.

1. Use the following data set of ages of 40 randomly selected employees at a corporation to answer parts A – F.

18 74 28 46 31 48 51 35 52 40 52 40 55 41 42 58 61 64 45

46 31 49 48 48 34 50 35 51 37 51 39 54 41 42 59 60 43 63 45 24

A. Construct a frequency table and a frequency histogram. Use 6 classes. And compute the Class Width, CW.

B. Based on the histogram, what is the shape of the distribution of employee ages?

_______________________________________________________________________________________________

________________________________________________________________________________________________

Frequency Histogram Frequency Table

Submit this answer sheet with your work!

Name:______________________________________________________________ SUMMER ‘19 Prof. DeSanto

MAT 102: DAH Exam 1 Form A

PART II: Place your answers on the provided answer pages. Be sure to answer all parts

C. Find the sample mean, median, mode, variance, range, coefficient of variation and sample standard deviation to the

nearest tenth.

mean:_____________ variance: _________________

median:___________ standard deviation: _________________

mode:_____________ coefficient of variation: _________________

range:_____________

D. On the following bell curve image, model the Empirical Rule by displaying the percent of ages that lie between

1, 2 & 3 standard deviations from the mean. THEN, answer the questions: D1 to D4.

D1. What percentage of the data falls within one standard deviation of the mean? __________________

D2. What percentage of the data falls within two standard deviations of the mean? _________________

D3. What percentage of the data falls within three standard deviations of the mean? ________________

D4. Does this data follow the Empirical Rule? Explain why or why not?

___________________________________________________________________________________

___________________________________________________________________________________

___________________________________________________________________________________

___________________________________________________________________________________

Submit this answer sheet with your work!

Name:______________________________________________________________ SUMMER ‘19 Prof. DeSanto

MAT 102: DAH Exam 1 Form A

PART II: Place your answers on the provided answer pages. Be sure to answer all parts.

E. Construct a box & whisker plot below and show the 5-number summary on the boxplot.

State the 5-Number Summary:

Min:____________ Lower Quartile:____________ Median:__________________

Upper Quartile:____________ Max:____________________

F. Based on your answers from part D & E, are there any outliers? Explain.

__________________________________________________________________________________________

__________________________________________________________________________________________

2. Professor Video, a college psychology instructor, wants to determine if there is a negative linear correlation between a

student’s GPA and the number of hours a student spends playing video games per week. She randomly selected twenty students

from all her classes and determined their number of hours playing video games per week and their GPA. The sample results

were:

GPA: 4.00 2.50 3.95 3.90 3.80 2.90 3.10 3.25 1.35 4.00

Hrs. Playing: 0 15 3 5 0 13 8 7 12 10

GPA: 1.95 2.75 2.98 2.90 1.50 2.20 3.00 3.15 2.70 2.80

Hrs. Playing: 12 13 11 10 17 9 6 8 13 16

(GPA SUMS: ∑X = 58.68 ∑X² = 183.7054) (HRS SUMS: ∑X = 188 ∑X² = 2214 )

2 a. State the Dependent variable and the Independent variable.

Dependent variable is: ______________________________________

Independent variable is: _________________________________________________________

Submit this answer sheet with your work!

Name:______________________________________________________________ SUMMER ‘19 Prof. DeSanto

MAT 102: DAH Exam 1 Form A

PART II: Place your answers on the provided answer pages. Be sure to answer all parts.

2 b. Label the axes and construct a scatter diagram

2 c. Compute the sample correlation coefficient, r. ____________________________________

2 d. Calculate the coefficient of determination & explain this result in terms of the dependent

and independent variable.

Explanation: ____________________________________________________________________

_______________________________________________________________________________

2 e. Write the Regression line equation for the relationship between a student’s GPA and the number

of hours a student plays video games per week.

______________________________________________________________________________

_____________________________________________________________________________

2 f. Use the Regression equation to predict the GPA of a student who plays 14 hours of video games

per week.

______________________________________________________________________________

_____________________________________________________________________________

Submit this answer sheet with your work!

Name:______________________________________________________________ SUMMER ‘19 Prof. DeSanto

MAT 102: DAH Exam 1 Form A PART II: Place your answers on the provided answer pages. Be sure to answer all parts.

3. According to a recent national Gallup Poll of U.S. smartphone user, 35% upgrade their cell phone every two years.

Use this information to answer the following questions. Show all work. Be sure to include your probability and calculator statements for the questions where indicated.

a. Determine the probability that exactly 9 users out of the 13 smartphone users upgrade their cell phones every two years.

Probability statement: Calculator Function w/values:

[State question using probability notation: P( )] [List TI calculator function with values used

to solve this problem.]

b. Determine the probability that at most 4 users of the 13 smartphone users upgrade their cell phones every two years.

Probability statement: Calculator Function w/values: [State question using probability notation: P( )] [List TI calculator function with values used

c. Determine the probability that between 7 and 9 users, inclusive, of the 13 smartphone users DO NOT upgrade their cell phones every two years.

Probability statement: Calculator Function w/values:

[State question using probability notation: P( )] [List TI calculator function with values used

d. Determine the probability that at least 1 user out of the 13 smartphone users upgrade their cell phones every two years.

Probability statement: Calculator Function w/values:

[State question using probability notation: P( )] [List TI calculator function with values used

e. Would it be unusual if more than 10 of the 13 smartphone users upgrade their cell phones every two years? Explain why or why not. Support your answer with pertinent probability calculations.

Probability statement: Calculator Function w/values:

[State question using probability notation: P( )] [List TI calculator function with values used

Submit this answer sheet with your previous work!

Name:______________________________________________________________ SUMMER ‘19 Prof. DeSanto

MAT 102: DAH Exam 1 Form A

Part I Answer Column

1.___________________ 11.___________________

2.___________________ 12.___________________

3.___________________ 13.___________________

4.___________________ 14.___________________

5.___________________ 15.___________________

6.___________________ 16.___________________

7.___________________ 17.___________________

8.___________________ 18.___________________

9.___________________ 19.___________________

10.___________________ 20.___________________

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