Mixture
What is Reject the Null Hypothesis
This is the decision you make if your p-value is less than your significance level (alpha).
How do you find expected count?
row * column/ total
What is (4-1)*(3-1) = 6?
If a two-way table has 4 rows and 3 columns, this is the number of degrees of freedom for the corresponding chi-square test.
What is the p-value?
A small one of these (typically less than 0.05) provides evidence against the null hypothesis in a chi-square test for independence, leading to the conclusion that there is an association between the variables in a two-way table.
A study examines the association between smoking status (smoker, non-smoker) and the presence of a certain gene (present,absent). Data is collected from a random sample of adults. What conditions must be met to perform a Chi-Square test for independence?
Random: The data must come from a random sample.
Independent: Individual observations must be independent of each other(10% condition if sampling without replacement).
Large Sample Size :All expected cell counts must be at least 5.
What is the Chi-Square Test for Independence?
This test is used to determine if there is a significant association between two categorical variables.
A researcher collects data on the preference for two types of snacks(chips,fruits) among two age groups(children,adults). The observed counts are as follows:
Children:Chips=30, Fruit=10
Adults: Chips=20, Fruit=40
Total for children=40, Total for adults=60,Overall Total=100
Expected count for Children(chips)=(40*50)/100=20
Expected count for Children(fruits)=(40*30)/100=12
Expected count for Adults(Chips)=(60*50)/100=30
Expected count for Adults(Fruits)=(60*30)/100=18
A researcher wants to determine if there's a relationship between a favorite subject in school and preferred learning style. They survey a group of students and categorize their responses into three subject categories(Math,Science,English) and four learning style categories(Visual, Auditory, Kinesthetic, Reading/Writing).
If the researcher performs a chi-square test for independence, what are the degrees of freedom?
(3-1)(4-1)=6
What is a Type I error?
This is the consequence of rejecting the null hypothesis when it is actually true, which can be controlled by setting an appropriate significance level.
Why is it important for the data to come from a random sample or a randomized experiment when performing inference for two-way tables?
Random sampling or a randomized experiment helps to minimize bias and ensures that the sample is representative of the population.
What is strong evidence of an association?
This is what a large Chi-Square test statistic indicates about the association between two categorical variables.
What is (50 \* 80) / 200 = 20?
If the row total is 50, the column total is 80, and the grand total is 200, this is the expected count for that cell.
A survey asks students whether they prefer online, in-person, or hybrid classes. The data is categorized by college major(STEM,Humanities,Arts). If we want to perform a Chi-Square test for independence to determine if there's a relationship between class preference and college major, how would you calculate the degrees of freedom?
There are 3 class preferences(online, in-person, hybrid) and 3 college majors(STEM,Humanities,Arts).
Df=(3-1)(3-1)=4
In a survey of 150 students, researchers want to determine if there is an association between students favorite subject(math,science,arts) and their study habits(cramming,regular study, no study).The Chi-Square Test yields a p-value of 0.15. What conclusion can you draw from this p-value regarding the null hypothesis?
What should you do if the "Large Counts" condition is not met when analyzing a two-way table?
If the "Large Counts: condition is not met, you may need to combine categories in the table or collect more data to increase the expected counts.
What is (number of rows - 1) \* (number of columns - 1)?
This is the formula for calculating the degrees of freedom for a Chi-Square test of independence.
What is (Row Total \* Column Total) / Grand Total?
This is the formula used to calculate the expected count for a cell in a two-way table.
A study examines the relationship between pet ownership and living situation. A sample of individuals is classified by whether they own a pet(Yes,No) and their living situation(Apartment,House,Dorm). The data is analyzed using a chi-square test.
What are the degrees of freedom for this test?
(2-1)(3-1)=2
What is the p-value?
This probability represents the chance of observing a test statistic as extreme as, or more extreme than, the one computed from the sample data, assuming the null hypothesis is true.
What is the independence condition?
When sampling without replacement, this condition ensures that individual observations are independent, typically verified by checking that the sample size is less than 10% of the population size.
What is the Chi-Square Distribution?
This is the distribution that the Chi-Square test statistic approximately follows when the null hypothesis is true.
What is the null hypothesis of independence?
* Answer: If the observed counts are far from these, it suggests evidence against the null hypothesis of independence.
* Question: What are expected counts?
Question 8:
* Answer: This is the formula used to calculate the expected count for a cell in a two-way table.
* Question: What is (Row Total \* Column Total) / Grand Total?
Question 9:
* Answer: The sum of these counts across any row or column will always equal the corresponding row or column total in the observed data.
*
This is the hypothesis that is assumed to be true when calculating expected counts in a two-way table.
What are the degrees of freedom?
The shape of the chi-square distribution depends on this value, which affects the critical value used for hypothesis testing with two-way tables.
What is "fail to reject the null hypothesis?"
If the p-value in a chi-square test is 0.30, this is the decision you would make regarding the null hypothesis at a significance level of 0.05.
What is the random condition?
This condition requires that the data be obtained from a random sample.