Exam 2 Terms Flashcards
What does a hypothesis test do?
A hypothesis test uses data from a sample to assess a claim about a population.
When do we not need a hypothesis test?
If we have data for the entire population.
Describe the null hypothesis.
- Contains an equality ( = )
- is in terms of parameters, not statistics
Describe the alternative hypothesis.
- sign can be not equal to, > , or <
- in terms of parameters, not statistics
What does it mean in the null hypothesis if rho = 0?
It means there is no correlation
rho represents a population correlation
What is the p-value?
The probability of obtaining results (in direction of the alternative hypothesis) as extreme as, or more extreme than, those observed if H0 is true.
If our p-value is small enough, then we have convincing evidence against H0 in favor of Ha.
p-value < alpha
reject the H0, results are statistically significant
p-value > alpha
fail to reject the H0, results are not statistically significant
Is failing to reject the null hypothesis the same as accepting it?
no, we never say we “accept” H0
What are the steps of testing a hypothesis?
- State H0 and Ha
- calculate sample statistics
- calculate the test statistic
- acquire p-value
- make a decision about H0 and Ha based on alpha
- write conclusion
What does t-distribution shape depend on?
sample size where degrees of freedom = n-1
What is the formula for test statistic?
t = x bar - mu / (s/sqrt n)
sample mean minus hypothesized population mean divided by the sample standard deviation over the square root of the sample size
What is standard error?
s/ sqrt n
How do we determine what “tails” to use when calculating p-value?
Equal tails in Ha does not equal whatever you’re testing (must multiply p-value by 2)
right tail if Ha > than what you’re testing
left tail if Ha < than what you’re testing
What assumptions must be met to use a t-test?
Sample size must be greater than or equal to 30
Data should be bell shaped with no extreme outliers
What p-value provides greater evidence against H0?
the smaller p-value
ex p = 0.0031 provides stronger evidence against H0 than p = 0.0032
What is alpha?
the significance level or probability of making a Type I error
can be assumed to be 95% (0.05) if not stated
If the sample mean is less than the hypothesized mean, will the t test statistic be negative or positive?
negative
If the sample mean is greater than the hypothesized mean, will the t test statistic be negative or positive?
positive
What happens to the test statistic as the difference between the sample mean and the hypothesized mean increases?
What happens to the p-value in this scenario?
Test statistic gets farther away from 0
The p-value gets smaller
What happens to the p-value if the test statistic is close to 0?
It gets larger