Z-tests and T-tests Flashcards
(29 cards)
What is the purpose of the Z-test?
To test differences between ONE SAMPLE and A POPULATION proportion or mean.
What are the null and alternative hypotheses for the Z-test for Proportions?
H0: No statistically significant difference between sample proportion (p) and population proportion (Π).
H1: A statistically significant difference between sample proportion (p) and population proportion (Π).
When is the Z-test typically used?
When the population standard deviation (σ) or proportion (Π) is known.
What is the formula for calculating the Z-test statistic for the mean?
Z = (X̄ - μ) / (σ / √n)
What is the significance level often set at in hypothesis testing?
5% (α < 0.05)
What does it mean if the Z-test statistic is outside the critical values?
Reject the null hypothesis (H0).
What is the critical value of Z for a significance level of 0.05?
±1.96
In the context of the Z-test for Proportions, what does a two-sided test imply?
The sample proportion could be larger or smaller than the population proportion.
What is the critical Z value for a one-sided test at a significance level of 0.05?
1.645
What happens when the population standard deviation is not known and the sample size is less than 30?
Use a One Sample T-Test.
Who invented the t-test and why?
William Gosset invented the t-test for quality control in brewing with small samples.
What does the degrees of freedom (df) indicate in hypothesis testing?
The flexibility or wiggle room in the data.
What is the relationship between the t-distribution and the normal distribution as sample size increases?
As sample size increases, the t-curve approaches the normal curve.
What do we need to assume about the sample when using the t-test?
The observations must be normally distributed.
Fill in the blank: The Z-test can be used when the population standard deviation is known and the sample size is _______.
30 or greater.
True or False: The Z-test can only be used when the population standard deviation is known.
True.
What is the conclusion when the calculated z-statistic is greater than the critical value?
Reject the null hypothesis (H0).
What happens to the t-curve as the sample size increases?
The curve gets taller and thinner.
When does the t-curve resemble the normal curve of the z-statistic?
When the sample reaches 30 or more.
What statistical software always calculates a t-test?
SPSS.
What do degrees of freedom (df) represent in a t-distribution?
The number of datapoints within a sample that are free to vary.
In a one-sample t-test, what is the formula for degrees of freedom?
df = n – 1.
What is the difference between a sample and a population?
Population is the entire group; sample is a subset selected to represent the whole group.
When is the Independent Samples T-Test used?
To compare two independently drawn samples from two groups.
