Stats Final Exam Flashcards
What type of data is collected through a count?
Discrete quantitative
What type of data is collected through measurement
Continuous quantitative
What type of data is categorical?
Qualitative
What are the 3 principles of experimental design?
- Control
- Randomization
- Replication
What is the difference between observation and experiment
- o= observe + take measurements, data that already exists
- e= impose treatments and controls// one variable is the cause of changes
This is an experimental condition that determine the levels of single/multifactors
experimental treatment
What is the sampling method used to eliminate bias?
Simple Random Samples (SRS)
What are 3 biased sampling schemes?
convenience sampling, voluntary response sampling, nonresponse sampling
A call-in radio show that solicit audience participation in surveys on controversial topics like abortion is an example of
voluntary response sample
This is a variable that is not the explanatory variable but is thought to affect the response variable
Confounding, lurking
When can confounding variables be a problem?
- The results show a false correlation btwn dependent and independent variables,
- Null hypothesis.
Why is control, randomization, + replication important?
differences in the results of an experiment are not attributed to chance but are caused by treatments.
How do you look at a histogram and find the median
- write the values on the graph
- Add them up
- +1
- divided by 2
Which measure of center is NOT resistant to outliers- Median or Mean?
The Mean
What does the z score measure?
whether the data value is above or below average in standard deviations
What is the symbol for correlation
r
In a scatter plot- what does it mean when the data points are spread apart
r value further away from 1
What types of variables must you use to compute the r value
quantitative values
What do the regression line and the correlation have in common?
both have the same sign (neg or pos)
What is included in a 5 number summary
- Min
- IQ1
- Median
- IQ3
- Max
If the scatter plot is curved is the regression line and r value appropriate?
no
What are the 3 percentages affiliated with the empirical rule? (if histogram is bell shaped)
68
95
99.7
How many standard deviations is 68% away from the mean?
1
How many standard deviations is 95% away from the mean?
2
How many standard deviations is 99.7% away from the mean?
3
What is the formula for the z score?
individual- pop mean / standard deviation
What is the value you get in the z-score mean
it is the number of standard deviations= correspons with the s.d. value
What are the steps to determine an outlier?
- IQR x 1.5
- Add that value to Q3
- Add value to Q1
- Evaluate new range and compare
What must you do before graphing a box plot?
determine if there are any outliers
In terms of scatter plot, what does bivariate mean?
2 quantitative variables being compared
Which value is the slope b0 or b1?
b1
How do you compute the y-intercept?
b0= yavg- ( b1 * xavg)
What tables do you need to get the sum for b1?
x, y, x - xavg, y - yavg, x - xavg2, y - yavg2
Sxy/Sxx
In the error sum of squares what new value are you computing?
the comparison of y actual and y with the equation
What does r2 measure
the percent of variation explained by observed values in response to the regression
the total sum of squares
is the total sum of variation in the response variable.
SSR or regression sum of squares
the variation explained by the regression
What indicates a strong linear relationship of r
value close to -1 or 1
Define a random experiment
an action whose outcome cannot be predicted with certainity. Each subject equally likely.
Define a sample space
the collection of all possible outcomes for an experiment
Define an Event
a collection of outcomes. A subset of a sample space.
Define mutually exclusive
2 or more events, no 2 having anything in common
Define independent events
may still have something in common, but does not affect the probability of the former event.
Define the complement of an event
1- the probability the evend does not occur. Not A
Descrime the union of 2 events
A can occur B can occur or Both can occur
What is the intersection of 2 events
A and B occur simultaneously
P(A) = 1 means..
the event is certain to happen
P(A) = 0 neabs
the event will NOT happen
What rule does this equation fall under:
P(A or B) = P(A) + P(B)
Special Addition for mutually exclusive events
The complementation rule formula
P(A) = 1 - P(not A)
What rule does this equation fall under:
P(A or B) = P(A) + P(B) - P(A + B)
General Addition Rule. Because it will always get you the right answer
What is a contingency table?
- the distribution of one variable in rows another in columns
- study the association between the two variables
the probability of one event occuring when it’s known that another one has occurred.
Conditional Probability
Finish the equation P ( B | A)=
P(A & B) / P(A). (Pay attention to the sample size.) General Conditional Rule.
When referring to the intersection of 2 events, What is the general rule?
P(A & B) = P(A) * P (B | A)
What is the special conditional rule-
When A & B are independent events. P(B | A) = P(B)
When referring to the union of 2 events. What is the special rule for independent events
P( A & B) = P(B) * P(A)
What is a random variable?
a numerical value that’s determined by chance
Define the probability distribution
the probabilities with which X takes those values
How to remember greater than and less than….
the pointy end is facing the smaller one ex 9 >6
When reading the equation, decide which formula to use before you plug in the equation
If two events are mutually exclusive, what is their probability?
0
If two events are independent what is the probabilty?
you must multiply them
Suppose E and F are 2 mutually exclusive event, with P(E)=0.4 and P(F)=0.2 then P(E or F) equals..
0.6
How would you write 5% of students who work full time are full time student
P(S|W) = 0.05
How do you explain in words when 2 events are dependent
P(S|W) does NOT equal P(S)
What would a venn diagram look like if Student A skips class and Student B does not skip class
What is the proportion formula for Z in terms of confidence interval
P(1 - P)/N, then SQUARE ROOT
Where does a density curve lie on a graph
the x axis
What is the total area under a curve?
1
What is a continuous probability distribution?
a density curve
How do you find the probability association with a normal distribution
- z = x - µ / σ
- then use the Table II
What is a percentile?
Solve for X “unstandardize”
x= µ + zσ
Define statistic
the value of a statistic will vary from one random sample to the next
If the x variable follow a normal distribution with µ and σ, then which rule applies?
68 - 95 - 99.7 %
Parameter
the value of a parameter remains constant
Define Sampling Error
- Because statistics are random variables
- a slight error associated with the estimate
- x - u
What is a sampling distribution
- a probability distribution for all possible samples
If the sample is from a normal poulation then what does x bar have?
a normal sampling distribution
What is σx?
= σ / square rt of n
How are probabilities found?
standardizing using the standard normal table
How are percentiles found?
by unstandardizing from the standard normal table
Define the Central Limit Theorem
- when the sample size n is large is a normal distribution
Define a point estimate?
- single number estimate
- give no indication of the size of the sampling error
Will the point estimate equal the true value?
No, because of sampling error
What does the margine of error indicate
how big the sampling error might be
What is a confidence interval?
a range of estimate for the true population parameter.
= Point Estimate +/- Margin of Error
What does level of confidence mean?
how certain we can be that the true value is contained in the interval (%)
What also increases as the level of confidence increases?
the width of the confidence interval
What happens to the width of the confidence interval when n increases?
the width decreases
If you are given the endpoints of a confidenct interval, how do you calculate the mean?
add and divide by 2
What weight sparates the value of the heaviest 10% al all books from the 90% (90th percentile) what type of question is this?
unstandardizing- look for Z in table II
If you are given *n * in a problem with mean and standard deviation, what is the first thing you need to do?
- convert σ to σx
- use z equation
- look up in table II
which equation do you use to obtain the confidence interval?
t-interval ch 8
When looking for a proportion, where can you find the equation?
Chapter 12- “z-interval for p”
For a hypothesis test, if the question says the words “true mean” which equation do you use?
When the equation says not equal what do you need to do?
- multiply T x 2, if its comparing u
- multiply P x 2, if it comparing 2 u values
If the P value is less than alpha what does that mean?
The greater the t value means
If the p value is greater than alpha, what does this mean?
if your using the t-interval for u. what do you do to finish the formula?
look up t value in table iv
when do you use the t-interval for u equation
when you do not know sigma (standard deviation)
