Lecture 7 Flashcards
Hypothesis Testing with One Sample
What are the steps in a hypothesis test?
- identify needed values (n, p-hat, p, s, x-bar, etc)
- set up null/alt, level of sig, and type of tail
- choose test statistic
- calculate test statistic
- based on tail test/alpha, determine crit. value
- compare test stat to crit.value and conclude
What is a two tailed test?
critical region is split into 2 ends (H1 not equal x)
Why are two tail tests preferred?
Because the rejection region is split in 2 (smaller area of rejection) thus are less likely to reject null/make accurate decision about rejecting null (less error)
What is a right tailed (upper) test?
critical region to the RIGHT end (H1>x)
What is a left tailed (lower) test?
critical region to the LEFT end (H1<x)
What is the significance level?
represents how much error is able to be held within the values of X% CI
Why are smaller p-values better?
a smaller p-value means there’s less error
When something is statistically significant, is the null rejected or accepted?
rejected
What two scenarios is the null rejected?
- when crit. value falls in crit.region
- when p-value is LESS than 0.05 (investigator’s findings are true)
What are the two types of error in hypothesis testing?
- type I error (null is true even though rejected, false positive)
- type II error (null is really false even though accepted, false negative)
How can type II error be minimized?
with a larger sample size
What does the p-value represent?
the probability of making a type I error
What is the test statistic for a single sample PROPORTION compared to a population?
z= p-hat - p / root (p*q/n)
- p-hat = x/n (sample proportion)
- p = population proportion in null
What two calculations are ran to assume the sample is normally distributed?
np and nq >= 5
How does one determine a P-value?
find where the calculated test statistic would hypothetically fit in the crit.values in the row of DF and determine if it would be found > or < of a certain confidence level
What is the test statistic for testing a claim about a sample MEAN >=30?
z = X-bar - mew0 / s / root n
What is the test statistic for testing a claim about a sample MEAN < 30?
t= X-bar - mew 0 / s / root n
In two sided tests, if the test statistic is a negative value, what must be true of the critical value?
it must also be negative
What is being compared in multinomial goodness of fit tests?
comparing observed values to expected ones
What is the X^2 (test statistic) equation?
X^2 = sum of [(O-E)^2 / E]
What are expected values based on?
based on the OPPOSITE of the claim being made
If all frequencies are expected to be equal, how are expected values calculated?
E = n (# of trials) / k (# of categories)
If all frequencies are NOT expected to be equal, how are expected values calculated?
E = n*p for EACH category
p = each category’s probability
Are preferred X^2 values small or large and why?
larger - proves there’s a difference from what is believed to be true
What is the relationship between X^2 statistic, test statistic, and p-values?
X^2 and test statistics are proportionally related (goes up/down together) and are both inversely related to p-values (as the stats increase or decrease, p-values does the opposite)
