Sampling + Bias
Type of sample where every nth unit is selected
Systematic Sampling
Does P(A) = P(A|B)?
Researchers want to ESTIMATE the difference in # of text messages sent each day by boys and girls. They find that 200 girls had an average of 220 w/ a SD of 50 and boys had an average of 110 w/ a SD of 35. What type of statistical analysis should be used?
2 Sample t Interval for Difference in Means
Conditions for 1 Prop Z Tests
Random Sample
Independent: n less than 10% N
Normal - np and n(1-p) are both greater than 10
p̂ vs p
Sample Probability vs Population Probability
Form of bias that fails to get input from some part of the population
Undercoverage Bias
How to calculate the probability of event A and event B?
(A ∩ B) = P(A) ∙ P(B|A)
A school claims that 12% of its students are out of uniform each day. You think this number is too high and want to test it at a significance level of α = 0.05. You take a sample of 80 students and find that 12 are out of uniform. What type of statistical analysis should be used?
One Proportion Z Test
A random sample of 20 individuals have an average of 20 books read a year. Does this meet the Central Limit Theorem?
No.
20 is less than 30
Q3-Q1 = ?
IQR = middle 50% of data
A pollster stands on a street corner and interviews the first 100 people who agree to speak to him. What kind of sampling is this?
How to calculate probability of event A OR event B?
P(A U B) = P(A) + P(B) - P(A ∩ B)
Your parents claim that you only study 65 minutes each night. You press them to prove it. They concur by recording your study time over 30 nights and find an average of 45 minutes and a SD of 10 minutes. Is there a significant difference? What type of statistical analysis should be used?
One Sample t Test for Means
A company will fire their manager if it is found that the proportion of sales made in a day is less than .5. An inference test finds that there is evidence for the alternate hypothesis that the proportion of sales made in a day is less than .5. What could be a possible error + consequence in this context?
Type 1 - reject the null when the null is true
The manager could be fired even though the sales are higher than the lower limit.
Sx vs σ
Sample Standard Deviation vs Population Standard Deviation
Form of bias where selected individuals fail to respond, cannot be contacted, or decline to participate
Nonresponse Bias
What kind of events cannot both occur? They have no outcomes in common.
Mutually Exclusive Events
You want to know if there is an ASSOCIATION between gender and the color of car driven. That is, do men prefer driving black vehicles vs. women driving white vehicles? What type of statistical analysis should be used?
Chi Square Test for Independence
100 people in sample. Probability of Success is .47. Does this meet the Large Counts Condition?
Yes!
100(.47) = 47 = greater than 10
100(1-.47) = 53 = greater than 10
x̄ vs μ
Sample Mean vs Population Mean
To survey voters in a town, a polling company randomly selects 10 city blocks and interviews everyone who lives on those blocks. What kind of sampling is this?
Cluster Sample
Events that do not influence each other's outcomes. One event has no effect on the next one
Independent Events
Researchers want to know if Coppertone is a more effective sunscreen than Banana Boat. They invite 30 subjects to participate. For each subject, they randomly select which arm gets Coppertone, and apply Banana Boat to the other. They compare the results at the 1% level of significance. What type of statistical analysis should be used?
Paired Difference of Means t Test
Conditions for X2 Tests
-random sample
-all expected counts greater than 5
-n less than 10% of N