Chpt 11 - Chi-Square Tests Flashcards
What test can be used to find out if a die is claimed to be unfair?
Chi squared test
What is the chi square distribution
Special type of right-skewed curve which depends on its degrees of freedom
Starts at 0 on the horizontal axis and extends indefinitely to the right, approaching, but never touching, the horizontal axis
What is the total area under the chi squared curve?
Equal to 1
What are the effects of degrees of freedom on a chi-squared curve?
The larger the degrees of freedom, the more the X2 curve looks like normal curves
What is the value of X2α?
The area of α to its right under the chi-square curve
Which table do we use to find the X2α value?
Table VII
What is the formula to determine the expected frequency for a chi-squared test?
E = np
E is the expected frequency
n is the sample size
p is the probability specified by Ho
What is the test statistic for a chi-squared test?
X2 = Σ(O-E)squared/E
O is observed frequency
E is expected frequency
What are the steps to a goodness-of-fit test?
- Set up the hypotheses
- Check the assumptions
- Decide significance level and find critical value
- Calculate the test statistic
- Compare the test statistic with critical value
- Interpret the result in the context of the question
What are the assumptions that must be checked for a chi-square goodness-of-fit test?
All expected frequencies are at least 1
At most 20% of the expected frequencies are less than 5
Simple random sample
What are the basics for the hypotheses for a chi-square goodness-of-fit test?
Ho: The variable has the specified distribution
Ha: The variable does not have the specified distribution
How do we determine degrees of freedom for a chi-squared goodness-of-fit test?
c-1
the number of categories - 1
If we are using the P-value to solve a chi-squared goodness-of-fit test, how do we determine if we reject the Ho?
If:
α > p value -> we reject Ho
α < p value -> we DO NOT reject ho
What is the rejection region of a chi-squared test and how do we determine if we reject Ho?
The critical value is X2α with df=C-1
The rejection region is the area to the right of the critical value
If the test statistic is larger than the X2a value, we reject Ho
If the test statistic is smaller than the X2a value, we DO NOT reject Ho
A six sided die is claimed to be unfair so we rolled the die 1200 times and observed the results. We are using a significance level of 5%.
Set up the hypotheses
Ho: The distribution of the outcome of rolling this die is P(X=x) = 1/6, x = 1, 2, 3, 4, 5, 6
Ha: the distribution is not the one as shown above
A six sided die is claimed to be unfair so we rolled the die 1200 times and observed the results. We are using a significance level of 5%.
Determine the significance level and critical value
α = 5% = 0.05
df = 6 category (one for each die) -1 = 5
Z2α = 11.070