Download Math 2 with Support

Math 2 with Support
Review – Sampling and Comparing Data
Name _______________________
MM2D1.a Pose a questions and collect sample data from at least two different populations.
1. Keyshon is collecting data to discover the average number of books that high-school boys read each week
in his town. Which sample below is the least biased?
a) a sample consisting of every tenth boy from an alphabetical listing of all students in his school only
b) a sample consisting of 50 randomly selected boys from each of the high schools in town
c) a sample consisting of 50 volunteers from each of the high schools in town
d) a sample consisting of students on Keyshon’s baseball team
For each of the following scenarios, tell what type of sampling was done (self-selected, convenience,
systematic, or random) and whether the sample is biased or unbiased and why.
2. A team wants to know who the fans think was the team’s most valuable player during the season. Fans can
vote on the team’s website.
3. The managers of a movie theater chain want to find the number of movies people in the community usually
see in a theater each month. The managers have the ticket seller at each theater survey customers when
they purchase their tickets.
4. The managers of a company with 500 employees want to know how the employees feel about some
proposed changes. The managers use a computer to generate a list of 50 employees to survey from a
database that includes all the employees.
5. A university is conducting a survey to determine whether a public library has hours that satisfies most of
their patrons. At the library, students survey every 10 th patron that exits the library.
6. A bicycling club wants to gather information about biking condition in the city. A survey for bicycle
riders is posted on club’s website.
7. A survey of the school’s lunch menu is being conducted. Every third student entering the cafeteria is
surveyed and asked “Do you think the lunch menu should include grilled chicken instead of pizza because
grilled chicken is healthier?”
MM2D1.d Compare the means and standard deviations of random samples with the corresponding
population parameters.
1. The class average on a math test was 75 and the standard deviation was 4.2. Find the z-score for a test
score of 68.
2. The heights of 3 year olds at a preschool averaged 32.4 in., with a standard deviation of 1.5 in. Estimate
the probability that a randomly selected 3-year-old is between 31.4 in. and 34.9 in. in height.
3. There are 150 volunteers at a hospital. Lian selected 10 random samples of 8 volunteers each and asked
them their ages. The sample means she found are shown below. What is a good estimate of the mean age of
the entire population of volunteers.
x
X
X
x
X
X
X
X
X
X
14
15
16
17
4. What does a normal distribution look like?
5. For a large population, the mean is 13.7 and the standard deviation is 8.9. One random sample produced
data values of 19, 8, 12, 17, 16, 25, 5, 18, 21, 7. Another random sample had data values of 12, 15, 17, 20, 13,
11, 18, 9, 15, 14.
a. Calculate the mean and standard deviation of the first sample.
b. Calculate the mean and standard deviation of the second sample.
c. Compare the means and standard deviations of the samples to the population mean. Are they the same?
Are they close? Are the samples representative of the population?
6. Does a sample have more or less variability than a population?
EOCT Practice
1. Your school newspaper is conducting a survey about music. Which survey question is least likely to lead to
biased results?
a) Do you listen to boring classical music?
b) What is your favorite type of music?
c) Do you agree that fun dance music should be played at school dances instead of loud rock music?
d) Do you, like most people your age, watch music videos?
2. A cosmetic company makes a face wash for 3 different skin types. The average number of bottles
produced each day is listed in the table. A quality control inspector needs to choose a sample of bottles to
inspect. Which method will most likely be representative of all the bottles?
Skin Type
Normal to Dry
Combination/Oily
Sensitive
a)
b)
c)
d)
Bottles
2200
1600
1200
For each type, choose the last 15 bottles produced
Randomly choose 25 of each type
Choose the first 50 bottles produced, regardless of type
Randomly choose 44 normal to dry, 32 combination/oily, and 24 sensitive
3. Central High School is spending a portion of their budget on upgrading the computers in the lab. The
school wants to survey a sample of the school population about the upgrades. Which of the following would
be the best way to obtain an unbiased sample of 100 students?
a) Have students fill out a voluntary survey at lunch. Collect the first 100 surveys.
b) Interview every 3rd person to enter a Computer Science class on Tuesday.
c) Put every student’s ID number into a computer and select 100 students at random.
d) Interview the first 100 students who come into the school from their buses.
4. Suppose the test scores on an exam show a normal distribution with a mean of 82 and a standard
deviation of 5. Within what range do about 95% of the scores fall?
a)
b)
c)
d)
72  x  92
77  x  87
67  x  97
77.9  x  86.1
5. During boot camp, the drill sergeant measured the weight of the men in his unit. He found the average
weight of the men to be 142 pounds and the standard deviation to be 14 pounds. If there are 100 men in the
unit how many men would be expected to weigh less than 128 pounds?
a) 32
b) 16
c) 5
d) 34