Probability
Complement
The probability of an event not happening.
A Geometrical distribution finds this.
What is the probability of a certain number of tries when stopping on the first success.
The Chi-Squared formula
∑((observed-expected)2)/expected
Proportion or mean? A study found that 25% of all people in Walpole take at least 1 AP class.
Proportion.
A coin is flipped 5 times, and always landed on heads, the probability of the next flip landing on tails is this.
50%
Free space!
Free points!
The probability formula of getting 4/5 successes with a 70% chance to succeed.
(0.7)4(0.3)
In this situation we use a Chi-Squared test for homogeneity.
Finding if there is a difference in the distribution of a variable in multiple groups/populations.
The Z generic score formula.
(Statistic - Parameter)/Standard error
r
What is the correlation coefficient.
Formula for finding a probability when all events are equally likely.
P(A)=(# of ways A occurs)/(total # of outcomes)
Binomial or Geometric? Two professional hockey teams tied their match for so long that it went into a shootout. Each team gets 5 attempts to score, what is the probability that the second team scores exactly 4 out of their 5 shots?
Binomial.
The generic hypothesis for a Chi-squared test for independence.
Ho: There is no association between (variable 1) and (variable 2) in the population of (context)
Ha: There is an association between (variable 1) and (variable 2) in the population of (context).
Correct hypothesis for: A national study found the average number of pets to be 1.5 per household. Caroline suspects her hometown owns less than the average number of pets.
Ho: mean = 1.5
Ha: mean < 1.5
A convenience sample is bad for this reason.
It doesn't get the opinions of everyone, generally the people it does get have a difirent opinion than the people who did not get sampled.
In order for a probability model to be valid, these two conditions must be met.
All probabilities add to 1, and every probability is between 0 and 1.
When finding the answer to a Geometrical problem on your calculator, plug in this.
geometpdf(p(success), x-value)
or
geometcdf(p(success), x-value)
For a chi-squared test for homogeneity or independence, how do you type it into your calculator?
2nd, matrix, scroll to edit, click enter on the first one, edit the size of the table then input the data.
The Z* value for a 95% confidence interval.
1.960
How to create a histogram on your calculator.
Input the data under the 'stat' button in L1 and L2, then do '2nd' 'y=' then turn it on and set it to a histogram using L1 and L2, then do 'zoom' and select the 9th option, 'ZoomStat'.
A store has multiple different brands available for each product. There are 3 brands of paper towels, 2 of detergent, and 5 of soap. A customer buys one of each of these products, how many different combinations of brands are there?
3 times 2 times 5 = 30 different combinations
The Binomial Formula.
(n/x)px(1-p)n-x
Which Chi-squared test is the most appropriate: A company that creates trail mix claims the following distribution of nuts, 12.5% peanuts, 38% almonds, 12.5% cashews, 10% hazelnuts, 12.5% Brazil nuts, 14.5% other.
Chi-squared test for goodness of fit.
Interpret the P-value at a=0.05 (alpha). An experiment for whether the true proportion of people in the town who think they are cool is greater than 80% had a P-value of 0.08. All conditions for inference were met.
Since the P-value of 0.08 is greater than a=0.05, we fail to reject the null. There is not convincing evidence that the true proportion of people in the town who think they are cool is greater than 80%.
Which linear regression model is the best? Model A has a slight pattern in the residuals and a R2 value of 0.65. Model B has no pattern in the residuals and a R2 value of 0.32. Model C has no pattern in the residuals and a R2 value of 0.72.
Model C