Definitions
Of the mean, median, and mode, which must be a value that actually appears in the data set?
Mode
If P= 0.03, would the result be statistically significant at the a = 0.05 level? What about a = 0.01?
A poll is conducted of 3500 households close to major national airports and another 2000 that are not close to an airport, in order to study whether living in a noisier environment results in health effects. Is this a randomized experiment or an observational study?
Observational study
Calculate the mean, median, and mode of this sample: 550 700 420 580 550 450 690 390 350
Mean: 520; median: 550; mode: 550
Find the critical value.
H0: µ=4 versus H1: µ > 4, n=25, a=0.05.invT (1-0.05, 25)= 1.71
Find the degrees of freedom given:
n = 24
n=3
df= 3-1=2
Central Limit Theorem
Sample mean of a large (n>30) simple random sample.
Sample mean has an approximately normal distribution.
When we check for normality, what do we assume?
1. We have a simple random sample
2. n>30, or the parent is approximately normal
What is a P-value?
The probability of observing a value for the test statistic that is as extreme as or more extreme than the value actually observed, under the assumption that the null hypothesis is true.
1. A fixed # of trials are conducted.
2. There are two possible outcomes for each trial (Success/failure).
3. The probability of success is the same on each trial.
4. Trials are independent (the outcome of one trial does NOT affect the outcome of the other trials).
5. The random variable X represents the number of successes that occur.
What is standard error also known as? How do you find the standard error?
Standard deviation.
population std. dev / square root of n
Define Type 1 and Type 2 Errors
Type 1: Reject the null hypothesis when it is true
Type 2: Failing to reject the null hypothesis when it is false