STATS module 8 Flashcards
What is the purpose of a single-sample t-test?
A single-sample t-test evaluates whether your sample mean is different from a reference value (e.g., “Is the sugar content of apples in my grocery store greater than 19 grams?”).
What question does a single-sample t-test answer?
Does the sample mean differ from the reference value?
What are the 4 steps of hypothesis testing in a single-sample t-test?
Define the null and alternative hypothesis.
Establish the null distribution.
Conduct the statistical test.
Draw a scientific conclusion.
How do you define the null and alternative hypotheses for a single-sample t-test?
No Directionality:
Ho: m=u
Ha: m ≠ u.
If there is directionality:
Ho: m ≤ u
Ha: m >u or vice versa.
What is the null distribution in a single-sample t-test?
The null distribution is sampling from a population where the mean equals the reference value (𝜇), and it uses a t-distribution (on a standardized scale).
How is the t-score calculated in a single-sample t-test?
m-u/s/sqrt(n)
m= mean
u= threshold
s=standard error
n=number of sampling units.
How do you interpret the p-value in a single-sample t-test?
If 𝑝 <𝛼, reject the null hypothesis.
If 𝑝≥ 𝛼, fail to reject the null hypothesis.
How should results of a single-sample t-test be reported?
Sample mean and standard deviation.
Observed t-score (two decimal places).
Degrees of freedom.
P-value (three decimal places).
EX: (t(197)=3.02, p=0.002).”
What is a paired-sample t-test used for?
To evaluates how a factor changes measurements within the same sampling unit (e.g., “Does fertilizing a crop improve yield?”).
How are null and alternative hypotheses defined for paired-sample t-tests?
No directionality:
Ho: d=u
Ha:d ≠ u
If there is directionality:
Ho: Difference = u
Ha: Difference ≠ u
How does the null distribution work for paired-sample t-tests?
The null distribution samples from a population where the difference between paired measurements equals the reference value (𝜇) and uses a t-distribution.
What is a two-sample t-test used for?
To compare the means of two independent groups (e.g., “Do eggs from free-range chickens have more protein than those from warehouse-raised chickens?”)
What is the null hypothesis for a two-sample t-test?
The null hypothesis states that the means of the two groups are equal (𝐻0: 𝜇1 = 𝜇 2)
What is the difference between hypothesis testing and estimation for a population mean?
Hypothesis Testing: Leads to rejecting or failing to reject decisions.
Estimation: Provides a numerical value for the population mean.
What are similarities between hypothesis testing and estimation?
1) Both use a sample to infer about the population.
2) Both rely on the sample being randomly selected.
3) Both use the sample mean and standard error in their calculations.
