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Exam 1 will cover Chapter 2-4.4

2. Open book, notes and calculator are allowed.

3. If you use notation that is different from the book and/or notes then a zero will be assigned for that

problem.

4. You must show all work for credit.

5. Do not use pen. Erase anything you do not want graded. Sloppy writing will incur penalties.

6. I prefer the exam to be printed out. If you cannot print out the exam, then write your solutions

on a blank piece of paper. If writing on blank paper, keep to the structure the way the exam

is written. Example: If there are three questions on the first page of the exam, then the

first page of your paper should have only three questions.

7. Your exam must be uploaded in pdf form under one file. It is very important when you

may not be graded and you will not be allowed to resubmit after the deadline.

9. You must submit the cover page with your honor code signature or it will not be accepted and it will

incur a late penalty.

Failure to follow any of the conditions will result in points taken off of your exam.

Honor Code Pledge:

I pledge that on my honor, as a Cerritos College student,

I have neither given nor received unauthorized assistance on this

exam.

Signature__________________________________________

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.

Solve the problem.

1) A school board member says, “The typical bus ride to school for a student living in the city limits is more than the

bus ride to school for a student living in the suburbs.” What does this statement mean?

A) If you are a student living in the city limits you will have a shorter commute time.

B) The center of the distribution of bus ride times for a city- dweller is more than the center of the

distribution for those living in the suburbs

C) All students living in the city spend less time riding the bus to school than those living in the suburbs.

D) There is less variation in the bus ride times of those living in the suburbs.

2) The U.S. Supreme Court Chief Justice data was used to create the following output in an Excel spreadsheet. Choose the

statement that best summarizes the variability of the dataset.

A) The age of most of the U.S. Supreme Court Chief Justice’s since 1900 are within 31.3 years of the mean age.

B) The age of most of the U.S. Supreme Court Chief Justice’s since 1900 are within 5.6 years of the mean age.

C) The ages of most of the U.S. Supreme Court Chief Justices are between 50 and 68 years.

D) None of these.

3) The mean can be thought of as the balancing point of a distribution. According to this description, at what value is the

following distribution balanced?

4) Below is the standard deviation for extreme 10k finish times for a randomly selected group of women and men.

Chose the statement that best summarizes the meaning of the standard deviation.

Women: s = 0.16 Men: s = 0.25

A) On average, men’s finish times will be 0.25 hours faster than the overall average finish time.

B) On average, women’s finish times will be 0.16 hours less than men’s finish times.

C) The distribution of men’s finish times is less varied than the distribution of women’s finish times.

D) The distribution of women’s finish times is less varied than the distribution of men’s finish times.

5) Below is the standard deviation for extreme 10k finish times for a randomly selected group of women and men.

Chose the statement that best summarizes the meaning of the standard deviation.

Women: s = 0.17 Men: s = 0.21

A) The distribution of women’s finish times is less varied than the distribution of men’s finish times.

B) The distribution of men’s finish times is less varied than the distribution of women’s finish times.

C)On average, men’s finish times will be 0.21 hours faster than the overall average finish time.

D)On average, women’s finish times will be 0.17 hours less than men’s finish times.

6) For the pair of histograms below, determine which distribution has the larger standard deviation.

B) (ii) has a larger standard deviation than (i).

C) There is no way to determine which one is larger.

D) Both histograms have the same standard deviation.

E) (i) has a larger standard deviation than (ii).

Use the empirical rule to solve the problem.

7) At one college, GPA’s have a distribution that is unimodal and symmetric with a mean of 2.6 and a standard

deviation of 0.5. What is the range of GPA’s from one standard deviation below the mean to one standard deviation

above the mean?

A) 2.6 to 3.1 B) 2.1 to 3.1 C) 0.5 to 3.1 D) 2.1 to 2.6

8) At one college, GPA’s have a distribution that is unimodal and symmetric with a mean of 2.6 and a standard

deviation of 0.5. Is a GPA of 3.8 more than one standard deviation above the mean?

A) Yes B) No

9) In 2007, the mean price per pound of lobster in New England was \$11.48 and the standard deviation was \$2.12. A

histogram of the data shows that the distribution is symmetrical. A local New England grocer is selling lobster for

\$8.99 per pound. What is this price in standard units? Assuming the Empirical Rule applies, would this price be

considered unusual or not? Round to the nearest hundredth.

A) z = 1.17; This is unusually expensive lobster. B) z = 1.17; This price would not be unusual.

C) z = – 1.17; This is unusually inexpensive lobster. D) z = – 1.17; This price would not be unusu

10) If Stacy worked 8.7 hours yesterday, would you consider this unusual?

A) Yes, 8.7 hours is more than 2 standard deviations above the mean.

B) No, 8.7 hours is less than 1 standard deviations above the mean.

C) Yes, 8.7 hours is more than 1 standard deviations above the mean.

D) No, 8.7 hours is less than 2 standard deviations above the mean.

11) Suppose we have a distribution of the number of “friends” all users of a popular social media site have.

What measure of spread would be best to describe this data?

A) spread should be described with the IQR because the distribution will be symmetric.

B) The spread should be described with the IQR because the distribution will be skewed to the right.

C) The spread should be described with the standard deviation because the distribution will be symmetric.

D) The spread should be described with the standard deviation because the distribution will be skewed to the

right.

12) The distributions of income in the United States is strongly skewed to the right. Which of the following is true?

A) There is not enough information to compare the median and mean values.

B) The median income is smaller than the mean income.

C) The median income is equal to the mean income.

D) The median income is larger than the mean income.

Use the side-by-side boxplots below to answer the question (#13-14). The boxplots summarize the number of sentenced

prisoners by state in the Midwest and West.

13) Pick the statement that best describes the shape of the distribution for the states in the West.

A) The data appears to be left- skewed with large variability.

B)The data appears to be right- skewed with a possible outlier.

C)The data appears to be roughly symmetrical with a possible outlier.

14) Based on the boxplot for the Midwest, which of the following is true?

A) 50% of the states sentenced less than 4,322 prisoners.

B) 50% of the states sentenced more than 29,928 prisoners.

C) 25% of the states sentenced more than 29,928 prisoners.

D) 25% of the states sentenced less than 1,435 prisoners.

The following boxplot contains information about the length of time (in minutes) it took women participants to finish the

marathon race at the 2012 London Olympics. (#15-16)

15) What can be said about the shape of the distribution of women’s running times for the marathon?

A) The distribution is right- skewed. B) The distribution is symmetric.

C) The distribution is unimodal. D) The distribution is left- skewed.

16) The fastest 25% of women participants ran the marathon how quickly?

A) More than 155 minutes. B) Less than 155 minutes. C) More than 160 minutes.

D) Less than 150 minutes.

17) Suppose temperatures and monthly ice cream sales were measured for 100 randomly selected cities.

Which variable is the explanatory variable and which one is the response?

a. Temperature is the explanatory variable and ice cream sales is the response because a city’s temperature

could explain the amount of ice cream sales.

b. Ice cream sales is the explanatory variable and temperature is the response because the ice cream sales

could explain the city’s temperature.

c. Ice cream sales is the explanatory variable and temperature is the response because a city’s temperature

could explain the amount of ice cream sales.

d. Temperature is the explanatory variable and ice cream sales is the response because the ice cream sales

could explain the city’s temperature.

18) Which scatterplot below depicts a stronger linear relationship? Why? Explain what the scatterplot shows

regarding a tree’s volume.

19) The scatterplot below shows the number of tackles received and the number of concussions received for a

team of football players for the most recent season. Choose the statement that best describes the trend.

A) Teams that receive a greater number of tackles tend to receive a lower number of concussions.

B) There is no association between the number of tackles a team receives and the number of concussions.

C) Teams that receive a greater number of tackles tend to have a higher number of concussions.

20) A study in the Los Angeles Times reported that the number of liquor stores in a neighborhood has a

strong positive linear association with the amount of crime in that neighborhood. What can you determine

about the relationship between the number of liquor stores and the amount of crime?

i. Neighborhoods with a higher number of liquor stores tend to have a higher amount of crimes.

ii. People who live in neighborhoods with more liquor stores commit more crimes.

iii. If we decrease the number of liquor stores in a neighborhood, the amount of crimes will decrease.

iv. No conclusions can be drawn without seeing a scatterplot of the data.

21) Which of the following statements regarding the correlation coefficient is false?

A) The correlation coefficient is a value between – 1 and 1.

B) A correlation coefficient of – 1 means that as one variable increases, the other decreases.

C) A high correlation coefficient tells us the data are linear.

Data were recorded for 117 months on a household’s gas bill (in dollars) and the average monthly temperatures for its

neighborhood. The mean monthly temperature was 48.7°F with a standard deviation of 20.6. The mean gas bill price

was \$81.20 with a standard deviation of 66.5. The correlation coefficient between monthly temperature and gas bill

price is -0.92.

22) Determine the correct value of the slope for the linear model that predicts gas bill price from monthly

temperature and interpret it in context.

a. The slope is – 2.97. For every one degree increase in monthly temperature, the gas bill price is predicted

to decrease by \$2.97.

b. The slope is – 0.28. For every one degree increase in monthly temperature, the gas bill price is predicted

to decrease by \$0.28.

c. The slope is – 2.97. For every one dollar increase in gas bill price, the monthly temperature is predicted

to decrease by 2.97°.

d. The slope is – 0.28. For every one dollar increase in gas bill price, the monthly temperature is predicted

to decrease by 0.28°.

The following linear regression model can be used to predict ticket sales at a popular water park.

Ticket sales per hour = – 631.25 + 11.25(current temperature in °F)

23) Choose the statement that best states the meaning of the slope in this context.

A) The slope tells us that a one degree increase in temperature is associated with an average increase in ticket

sales of 11.25 tickets.

B) The slope tells us that high temperatures are causing more people to buy tickets to the water park.

C) The slope tells us that if ticket sales are decreasing there must have been a drop in temperature.

D) None of these

24. Twenty students, selected at random were asked to estimate the number of hours that

they had spent studying in the past week (in and out of class).

The responses are recorded below.

15 58 37 42 20 27 36 57 29 42 51 28 46 29 58 55

43 40 56 36

a) Complete the table below

Hours Frequency Relative Frequency

10-19

20-29

30-39

40-49

50-59

b) Construct a frequency histogram and determine the shape of the distribution.

25. Suppose exam grades were recorded for 20 students in the class, but one of the

grades is no longer readable. If the mean score on the exam was 80 and the mean

of the 19 readable scores is 82, what is the value of the unreadable score?

26. The acidity or alkalinity of a solution is measured using pH. A pH less than 7 is

acidic; a pH greater than 7 is alkaline. The following data below represent the

pH in samples of bottled water and tap water.

a) Use your calculator to determine the mean and median pH for each type of water.

State answer to two decimal places.

Tap Bottled

Mean: Mean:

Median: Median:

b) Suppose that a pH of 7.10 in tap water was incorrectly recorded as 1.70.

How does this affect the mean? the median?