Margin of Error
When researchers look at unbiased sample sizes and apply it to the population, they are 95% certain that the results are within
the margin of error from their percentage. (Similar to being within 2 standard deviations from the mean)
Percentage – Margin of Error < x < Percentage + Margin of Error
Example 1: Candidate Koesters has a 76% approval rating with a 6% margin of error.
76-6 = 70 76 + 6 = 82
We are 95% certain that between Koesters has an approval rating between 70% and 82%.
Example 2: Senator Smith and Miller are in a close election. Senator Smith is projected to get 52% of the vote with a 5% margin
of error.
a. What is the highest amount of the vote that Smith is projected to get? 52+ 5 = 57%
b. What is the smallest amount of the vote that Smith is projected to get? 52-5 = 47%
c. What is the highest amount of the vote that Miller is projected to get? If Smith gets 47% then Miller would get 53%
Example 3: The percentage of people who speed through a town is between 35% and 43%. Find the mean percentage of
people who speed and the margin of error:
35…….Mean……43.
You go a distance of 8 divided by 2 spaces so the margin of error is 4 and the mean is 39.
Problems:
1. The senate has an approval rating of 15% with a margin of error of 4.2%. What is the 95% certainty range of their
approval rating?
2.
Candidate Hunter has a 83.2% approval rating. What is the 95% certainty range of her approval rating?
3.
Skittles estimates that 20.4% of its Skittles are red with a 2.1% margin of error.
a. What is the highest amount that could be red?
b. What is the lowest amount that could be red?
Prior to the 2008 election, President Obama was projected to get 51% of the vote with a 4% margin of error. Explain
why Senator McCain still had optimism prior to election night.
4.
5.
A candidate’s 95% certainty range for his approval rating is from 62-74%. Find the margin of error and his current
approval rating.
6.
Researchers are 95% confident that between 70% and 77% of the population wear seatbelts. What is the margin of
error and what is the approval rating?
7.
The margin of error can be found by the following formula: M.E= 2√
a.
b.
number of people. Find the margin of error of the following:
A candidate is predicted to get 54% of the vote based on a survey of 200 people.
A candidate is predicted to get 54% of the vote based on a survey of 2000 people.
8.
Does having a larger sample size create a larger margin of error or a lower margin of error?
𝑝(1−𝑝)
𝑛
where p is the mean percentage is n is the
Review Problems:
9-13. The number of ‘hits’ that Google receives each minute varies according to a normal distribution with a mean of 80,000 and
a standard deviation of 4,000.
9. What is the probability that Google with get between 76,000 and 88,000 hits a minute?
10. What is the probability that Google will get at least 72,000 hits a minute?
11. What is the percentile of a minute that Google gets just 76,000 hits?
12. What is the probability that Google will get between 73,000 and 81,000 hits? (use calculator)
13. Between how many hits will Google receive 95% each minute?
14. Workers at a large company have ages that vary to a normal distribution. If 68% of the workers have ages centered
about the mean of 32 and 53, what is the mean age and the standard deviation?
15. A cat’s weight of 13 is three standard deviations below the mean. A cat’s weight of 19 is one standard deviation above
the mean. Find the mean and the standard deviation.
16. A cow’s daily production of milk is 2 quarts with a standard deviation of .3 quarts. A goat’s daily production of milk is 1
quart with a standard deviation of .2 quarts. One day, a cow gave 2.6 quarts and a goat gave 1.6 quarts of milk. Which
is more remarkable? Explain.
Determine which research design (Survey, Observation, Experiment) should be used:
17. Researchers want to know the different effects between dieting and weight loss
18. Researchers want to know if there is a difference between the gender of workers and their level of job satisfaction.
19. Researchers want to know if there is an association between age and television viewing habits.
Are the following biased or unbiased. If it is biased then rewrite the scenario to make it unbiased.
20. Surveyors ask people entering the Carolina Panthers game who their favorite NFL team is.
21. Surveyors ask people, “Do you prefer delicious spaghetti or soggy lasagna?”
22. There are 2400 at Middle Orange High School. Researchers ask a total of 200 students from all grade about their
opinion of the principal.
23. Surveyors ask “Don’t you agree that teachers in your school should earn more money?”
Determine which sampling method is used (Stratified, Random, Cluster, Convenience, or Systematic)
24. A teacher asks every fourth students walking into class a question
25. A teacher selects the first two rows to answer a question
26. A student assigns each of his social media friends a number and then chooses 100 random numbers
27. A teacher asks 20% of the males and 20% of the females in her class a question.
28. A teacher randomly assigns each student a group of A,B,C or D. She randomly selects group C and then randomly
selects 5 members from C.
29. Suppose you are studying if people prefer eating more expensive healthier and organic food or regular food. Give an
example of where convenience sampling would be biased and an example where convenience sampling could be
unbiased.
You have 46 vegetables in your yard (10 pumpkins, 16 tomatoes, and 20 cucumbers). You want to study the amount of bacteria
on each vegetable. You select 23 vegetables and find that they have an average of 2123 strands.
30. Identify the following:
Parameter: _______________ Population:________________
Statistic:__________________ Sample:___________________
31. Give an example on how you would use stratified sampling to select the 23 vegetables.
32. Give an example on how you would use systematic sampling to select the 23 vegetables.