Sampling & Study Design
What type of study applies a treatment and observes its effects?
An experiment
The data set is: 4, 6, 7, 9, 14
Find the mean and median.
Mean: 8.0
Median: 7.0
Joy Milne gained international attention when she claimed she could do what?
Smell Parkinson's Disease
A jar contains 6 red, 4 blue, and 10 green marbles.
What is the probability of randomly selecting a green marble?
1/2 or 0.5
The most commonly used graph to show frequency distributions. It looks like a bar chart (but is not!). You must have quantitative data to use it.
Histogram
//Make sure you know how to construct one
This sampling method selects every kᵗʰ individual from a list.
Systematic sampling
The variance on the last Statistics test was 0.59. This means that the standard deviation was what?
(Round to the nearest hundredth)
0.77
If you know your rounding rules, you know that two divided by three is ....? (Round to the nearest hundredth)
0.67
Write the following using probability notation, "The probability of getting the flu, given that it is January, is 70%".
P(Getting the Flu | January) = 0.7
Draw a histogram that is right skewed.
//Graph with data frequencies highest on the left side, with data tapering off to the right.
Which sampling method divides a population into subgroups and randomly samples from each?
Stratified sampling
The test scores are: 55, 60, 65, 70, 95
a) Find the median
b) Find the midrange
c) Explain why these two measures are different.
Median = 65.0
Midrange = (55 + 95) / 2 = 75.0
The midrange is affected by extreme values; the median is resistant.
The smallest prime number is...
2
In a class:
40% of students play soccer
25% play basketball
15% play both sports
What is the probability that a randomly selected student plays soccer or basketball?
P(soccer or basketball) = 0.4 + 0.25 - 0.15
0.50
Name two reasons a graph might be misleading.
Vertical axis not starting at zero; pictographs exaggerating differences.
There are three components that strengthen experimental design and reduce bias. Name two of them.
Two from:
Randomization, replication, and blinding
A data set has a mean of 50 and a standard deviation of 4.
Find the z-scores for the values 42 and 58, and state which value is more unusual.
z₄₂ = (42 − 50)/4 = −2
z₅₈ = (58 − 50)/4 = 2
Both are equally unusual. (Same distance from the mean.)
A survey of the entire population is known as a ...
Census
A company finds that 8% of its products are defective.
If two products are randomly selected, what is the probability that both are NOT defective?
(Assume independence.)
Probability one is not defective = 1 − 0.08 = 0.92
P(both are not defective) = 0.922 = 0.8464
0.8464
Give an example of a data set that is normally distributed.
Give an example of a data set that is right skewed.
Normal: Height, weight, IQ, blood pressure,...
Right skewed: Income, wealth, NBA salaries,...
Ms. Goldstein experiments with a new tennis serve technique. She finds that after use, she makes 99% of her serves. There is a 20% likelihood that this is due to chance. Is the outcome statistically significant? Explain why.
No, it is not statistically significant.
There is a 20% likelihood that Ms. Goldstein achieved this serving rate by chance. Because 20% is not less than 5%, we cannot conclude that it is statistically unlikely due to chance.
The following data represent the number of hours studied by students: 2, 12, 3, 8, 4, 5
a) Find the 5-number summary
b) Find the IQR
Minimum = 2
Lower half: 2, 3, 4 → Q1 = 3
Median = (4 + 5)/2 = 4.5
Upper half: 5, 8, 12 → Q3 = 8
Maximum = 12
IQR = 8 − 3 = 5
First semester Statistics class had assessments on the four major units and three related projects.
Name them all.
Assessments:
1) Intro to Stats, 2) Exploring Data w Tables & Graphs, 3) Descriptive Stats, 4) Probability
Projects:
1) Choc Chip Cookie Study, 2) Descriptive Stats Project, 3) Probability: Two Case Studies
In a class of students:
12 ate breakfast, 2 did not
11 like waffles, 3 do not
-all 3 students who do not like waffles ate breakfast
Are the events "like waffles" and "ate breakfast" independent events? Show how you know.
No, they are not independent events.
Knowing a student ate breakfast decreases the likelihood that they like waffles.
P(likes waffles) = 0.7857
P(likes waffles | ate breakfast) = 0.75
P(likes waffles | didn't eat breakfast) = 1
//These are not equal
Make a frequency distribution from the following data:
12 18 25 34 29
21 16 27 31 24
19 22 28 35 17
Use 5 classes.
Variable (x) | Frequency
12 - 16 | 2
17 - 21 | 4
22 - 26 | 3
27 - 31 | 4
32 - 36 | 2