Name ______________________________________
Date __________
Algebra 2: 11.4 Margin of Error and Confidence Intervals HW Day 2
True/False (1 – 2):
_____ 1. The margin of error is based on the standard deviation.
_____ 2. r1 standard deviation results in a 95% confidence interval.
Fill in the blank (3 – 8):
3. If you increase the size of your sample, then the confidence interval will _______________.
4. If you increase your confidence from 90% to 99%, then the interval will _______________.
6. If your sample has a larger standard deviation, then the interval will ________________.
7. If a data set with a mean of 4.5 has a standard deviation of 2.5, the 95% confidence interval is
_______________________.
8. The margin of error for the data set and confidence interval described in #7 is ___________.
9. A data set is found to have a mean of 8 and a standard deviation of 3. In your own words,
describe what the 99.7% confidence interval represents.
10. In a survey, teenagers were asked to rank the importance of their
relationship with their parents. The response scale ranged from 1 to
5, with 5 being extremely important. Use the information in the
table to decide which sample was most likely the greatest in size.
Explain your answer.
11. A researcher wants to investigate the number of hours high school students spend doing
homework each night. After surveying 1,200 high school students, the researcher makes the
claim that she is 95% confident that the number of hours students spend doing homework each
night is between 0.6 and 2.8 hours.
a. What is the mean and margin of error for this confidence interval?
b. What is the 99.7% confidence interval?
Name ______________________________________
Algebra 2
11.5 Linear Regression and the Correlation Coefficient
1. A supervisor of a cleaning business has the data in the table that shows the age of her
workers and the number of sick days they take each year.
a. Calculate the linear regression equation for this data.
b. Calculate the correlation coefficient.
c. Is the line a good fit for the data? How do you know?
d. Predict the number of sick days for an employee who is 50 years old.
e. Predict the age of an employee that uses 31 sick days each year.
2. A sales associate wants to know if there is a relationship between the average number
of times his coworkers contact clients each month and the average monthly sales
volume in thousands of dollars.
a. Calculate the linear regression for this data.
b. Calculate and interpret the correlation coefficient.
c. Predict the sales if clients are contacted 35 times in one month.
3. The data in the table represents the American College Test (ACT) composite scores and
grade point averages (GPA) of 20 randomly selected students after their first semester
in college. A college counselor wants to determine if there is a correlation between ACT
scores and first semester GPAs.
a. Calculate the linear regression for the data.
b. Calculate and interpret the correlation coefficient.
c. Use your linear regression to predict the GPA of someone who scored a 24 on the
ACT.
7. Use the graphs to estimate the mean and standard deviation of each distribution.
8. The weights of 1000 Chihuahuas were recorded on their first birthdays. The weights are normally distributed with
mean 10.3 kg and standard deviation 1.6 kg.
a. What is the probability that a randomly selected child will weigh less than 11.9 kg?
b. What is the probability that a randomly selected child will weigh between 8.7 kg and 11.9 kg?
c. How many of the 1000 children would you expect to weigh between 5.5 kg and 13.5 kg?
d. How many of the 1000 children would you expect to weigh more than 8.7 kg?
9. Which could be a possible source of bias: Christa wants to determine whether male or female students are more
likely to ride their bike to school. She waits at the entrance of school and records the gender of every student who
locks a bike at the bike rack.
[A] She needs to know what type of lock students are using.
[B] She included friends who ride their bikes.
[C] She needs to ride her bike to school
[D] She needs to know how many students of each gender there are in the whole school.
10. Decide whether the variable is a statistic, parameter, neither or both: The gross weight of fish caught by a trawler.
[A] Statistic
[B] Parameter
[C] Neither
[D] Both
11. Use the data sets for practicing linear regression.
a. Derive a linear model for the data, rounding to the thousandth.
b. Use the linear model to predict revenues if 121 patrons attend.
c. What is the value of the correlation coefficient?
d. Does your correlation coefficient suggest your line is a good fit? Why?
e. In general, what do correlation coefficient values indicate?
12. In a statewide poll 103 out of 500 Washingtonians rated themselves die-hard UW curling fans. If the standard
deviation is 8 Washingtonians, find the confidence interval for 68% and 99.7% confidence.
13. Media research wanted to estimate the mean amount of time (in minutes) that full-time college students spend
watching TV each weekday. The researchers surveyed 100 students outside the freshman dorm and found a sample
mean of 135.6 minutes and a standard deviation of 40 minutes.
a. What is one possible source of bias?
b. What is the margin of error for the 95% confidence interval?
c. What is the margin of error for the 99.7% confidence interval?
d. Johnny is an Honors Engineering student and estimated he watches 35 minutes of TV every weekday. What is
his z-score?
14. On a recent study on NBA Player Scoring Per Game (ppg), the normally distributed data had an average of 17 ppg,
with a standard deviation of 4.3 points.
a. Kevin Durant averages 28.1 points per game, what is his z-score?
b. If Stephen Curry has a z-score of 3.047, how many points per game does he average?
c. Brian Scalabrine’s average ppg is better than 2.5% of the leagues. How many points per game does he average?