Binomial distributions Flashcards
what does random variable X represent?
count of successes in n independent trials
When is an experiment considered Binomial?
- when fixed no. trials n where outcome is either success or fail
-outcome recorded is no. successes - outcome of each trial independent of the others
- prob of success in each trial is constant
What is binomial notation?
X~B(n,p)
n is no. trials
p is probability
x is outcome
how do you calculate binomial probabilities?
calculator:
distribution - binomial - parameters
what are cumulative binomial probabilities?
where X is greater than or equal to/less than or equal to an outcome found by working with distribution on calculator
what to be careful of in cumulative frequencies?
if its grtr. eq/ less eq. or just grtr/less - calculators. always opt for ‘or equal to’ so may need to add/subtract one
what is a hypothesis?
a statement made about the value of a population parameter that we wish to test by collecting evidence in a sample
what is the null hypothesis, Ho?
default position, nothing has changed until proven otherwise
what is a test statistic?
the evidence from a sample
what is the alternative hypothesis, H1?
there has been a change in the population parameter
what is the significance level?
maximum prob. where we would reject Ho
step 1 of hypothesis test?
define test statistic X, stating distribution and parameter p
step 2 of hypothesis test?
write null and alternative hypotheses
step 3 of hyp. test?
determine prob. of observed test statistic (or more extreme) assuming Ho - Ie. determine prob. it didn’t just happen by chance
step 4 of hyp test?
2 part conclusion:
- do you reject Ho or not?
- put into context of original problem
what do with 2 tailed hyp tests?
half sig level and deduce which tail you need to focus on (find mean, np and see which side bias lies)
how do you compare sig levels to probs?
multiply prob by 100 to get a percent, if less than sig level, reject Ho, if greater accept it
what is the critical region?
range of values for test stat that would reject Ho
what is critical value?
first value to fall within critical region
what is actual significance level?
actual prob. of being in critical region and incorrectly rejecting Ho
the prob of critical value as a percentage
What are the two different ways of identifying a critical value?
On hypothesis tests, the critical value will either be the first value of X who’s probability of incorrectly rejecting H₀ (test stat prob) is less than the sig. level or the Q may ask to find the value with the closest prob to the sig. level (can be slightly less/greater than)
