Describing Scatterplots
Calculating Regression Lines
Sampling Techniques
Everything bout Experiments
Definitions
100
Lydia wanted to know if sons of taller fathers tend to be taller. Here are the heights of the fathers and sons in Lydia's sample:
Weak positive linear association with potential outliers
100
A long jump competition took place recently at a local high school. The coach is interested in performing as well as possible next time, so he is looking at the relationship between height and distance jumped (both measured in inches). He uses height to predict distance.
The least square solution is:
intercept = 6.4285, and slope = 1.0534.
What is the estimated regression line (in context)?
predicted distance = 6.4285 + 1.0534(height)
100
A person researching education levels within a company takes the full employee list and applies a random number algorithm to this in order to select people to interview. |
Simple Random Sample
100
What is this an example of?
Randomized Block Design
100
________________ refers to the fact that different random samples of the same size from the same population produce different estimates.
sampling variability
200
Abigail gathered data on different teams' winning percentages and the average yearly salary of their head coaches (in millions of dollars). Here are her results:
weak positive linear association with potential outliers
200
A long jump competition took place recently at a local high school. The coach is interested in performing as well as possible next time, so he is looking at the relationship between height and distance jumped (both measured in inches). He uses height to predict distance.
Interpret the slope when b0 = 1.0534.
As height increases by one inch, distance increases by 1.0534 inches.
200
A high school student who is studying year-ten attitudes in the school uses registration tuition classes as strata and studies a random selection of students from each of these classes. |
Stratified Sampling
200
A drug company wants to test a new pill that should make people's nails grow twice as quickly as normal. How can they make the study a blind study?
Give one group of people the actual pill and one group a placebo, but don't tell the participants which pill they are receiving.
200
When the observed results of a study are too unusual to be explained by chance alone, the results are called __________________.
statistically significant
300
The manager of a factory wants to see if there is a relationship between safety and output. For 111111 days, they track the output of the factory and give each day a safety rating. Here are results:
Strong positive linear association with no outliers
300
The city’s transportation department is interested in studying the relationship between the temperature and the number of passengers that ride the main bus line in order to better serve their customers. The manager recorded the temperature at the beginning of the hour, and then had a bus driver record the number of passengers that boarded the bus throughout the hour.The manager wishes to predict the number of passengers using temperature.
Variable Mean SD
temperature 43.2 5.94
passengers 175.2 23.52
Correlation: r = 0.9984
Use the above information to obtain a least squares regression equation (in context).
predicted passengers = 4.43 + 3.953(temperature)
300
In a study of the opinions of homeless across a country, rather than study a few homeless people in all towns, a number of towns are selected and all of homeless people are interviewed in each one. |
Cluster Sampling
300
Half of the participants are given the medication, and the remaining participants are given a placebo. By utilizing a placebo, the study remains free from being altered as neither the participants nor the researcher knows who is receiving the medication. This provides valid and reliable results.
What is this an example of?
Double blind experiment
300
A ____________ is the difference between the actual value of y and the value of y predicted by the regression line.
residual
400
Ian wants to figure out there is a relationship between how much a piece of furniture weighs and how much it costs. He samples some items and comes up with the following scatterplot:
Moderately strong positive linear association with no outliers
400
Predict the number of passengers when temperature is at 45 degrees for the least squares regression line:
passengers = 4.43 + 3.953 temperature
182 passengers (182.3 exact)
400
A study of people going to night-clubs first determines that there are about 250-300 people in the club (due to fire regulations). A sample size of 30 is selected, giving an interval of 300/30 = 10. A random number between 1 and 10 is generated and comes up with 7. Starting with the 7th person to enter the club, every 10th person is given a brief interview. |
Systematic Sampling
400
What is this an example of?
Matched Pairs Design
400
The _______________________ measures the size of a typical residual. That is, s measures the typical distance between the y values and the predicted y values.
standard deviation of the residuals s
500
An author wants to find out if there is a relationship between how many copies of a book they sell and how many ratings below three stars the book gets. Here are their results:
strong negative linear association with potential outliers
500
temperature passengers
42 173
37 149
46 185
30 123
50 201
43 174
43 175
46 188
46 186
49 198
Given the information above, can you predict the number of passengers when temperature is at 65◦F?
65◦F falls beyond the x data range. If you used the above regression equation to ‘predict’ the number of passengers, then you basically made a unproved assumption. (Extrapolation)
500
A group of students in a high school do a study about teacher attitudes. They interview teachers at the school, a couple of teachers in the family and few others who are known to their parents. |
Convenience Sampling
500
Twenty men and 20 women with migraine headaches were subjects in an experiment to determine the effectiveness of a new pain medication. Ten of the 20 men and 10 of the 20 women were chosen at random to receive the new drug. The remaining 10 men and 10 women received a placebo. The decrease in pain was measured for each subject. The design of this experiment is
randomized block, blocked by gender
500
A _______________ measures an outcome of a study.
response variable