Statistics - Chapter 10
What is the approximate mean value of F for for all F-distributions?
1
What is the area under the curve in a chi-squared distribution?
1
What is the total area under the curve of an f-distribution?
1
What conditions must be met in order to use a two-sample F-test?
1. samples randomly selected 2. samples independent 3. each population normally distributed
What conditions are necessary to use the chi-square goodness-of-fit test?
1. the observed frequencies must be obtained randomly 2. each expected frequency must be greater than or equal to 5.
What do you call the intersection of a row and column of a contingency table?
A cell
Define multinomial experiment
A probability experiment consisting of a fixed number of independent trials in which there are more than two possible outcomes for each trial. The probability for each outcome is fixed and each outcome is classified into categories.
Calculating the expected frequencies in a chi-square goodness-of-fit test requires what assumption?
Assume the null hypothesis is true
T/F If the test statistic for the chi-square independence test is small, you will, in most cases, reject the null hypothesis.
False
T/F When the differences between the observed frequencies and expected frequencies are small, the chi-square test statistic is large.
False small differences = small chi-squared
T/F A small chi-square test statistic is evidence for rejecting the null hypothesis.
False, a large chi-squared test statistics is evidence for rejecting the null hypothesis
T/F for all F-distributions, the mean value of F is approximately 0
False, approximately 1
T/F the chi-squared distribution is normally distributed
False, it is positively skewed
T/F the test statistic for a chi-square goodness-of-fit test is always a left-tailed test
False, it's always a right-tailed test
T/F the test statistic for a chi-square goodness-of-fit test is always a two-tailed test
False, it's always a right-tailed test
T/F In a two-sample F-test, the larger variance is always in the denominator
False, the larger variance is always in the numerator
T/F in a chi-squared test, the sum of the observed frequencies must be less than the sum of the expected frequencies
False, they must be equal
Explain how to find the expected frequency for a cell in a contingency table.
Find the sum of the row and sum of the column the cell belongs to. Multiply these two sums and divide by the sample size.
State the null and alternative hypotheses for a one-way ANOVA test.
Ho: all population means are equal Ha: at least one of the means is different from the others
What is used to calculate the test statistic for the chi-square goodness-of-fit test?
Observed frequencies and expected frequencies
Explain how to find the critical value for an F-test.
Specify the level of significance. Determine the degrees of freedom for the numerator and denominator. Find the critical value of F.
T/F A large chi-square test statistic is evidence for rejecting the null hypothesis.
True
T/F If the test statistic for the chi-square independence test is large, you will, in most cases, reject the null hypothesis.
True
T/F In a two-sample F-test, the larger variance is always in the numerator
True
T/F When the differences between the observed frequencies and expected frequencies are large, the chi-square test statistic is also large.
True
T/F all values of x^2 are greater than or equal to zero
True
T/F in a chi-squared test, the sum of the observed frequencies must exactly match the sum of the expected frequencies
True
T/F the chi-squared distribution is positively skewed
True
T/F the formula for the chi-squared test statistic is the same for the goodness-of-fit test and the independence test
True
T/F the test statistic for a chi-square goodness-of-fit test is always a right-tailed test
True
Define one-way analysis of variance
a hypothesis testing technique that is used to compare means from three or more populations
Define two-way analysis of variance
a hypothesis-testing technique that is used to test the effect of two independent variables, or factors, on one dependent variable
T/F the f-distribution is symmetric about the mean
false, it is positively skewed
What is the degrees of freedom when using the chi-squared test?
k-1 k is the number of categories
In a two-sample F-test, the larger variance is always in the (numerator or denominator).
numerator
What to use to compare the means from three or more populations?
one-way analysis of variance
Describe the shape of the F-distribution
positively skewed, all values greater than 0, area under the curve is 1, mean is approx 1
To begin a goodness-of-fit test, what must you do first?
state a null and an alternative hypothesis
What is the expected frequency (E) of a category when calculating the chi-squared test statistic?
the calculated frequency for the category, found using the expected distribution and sample size
What is the observed frequency (O) of a category when calculating the chi-squared test statistic?
the frequency (count) for the category observed in the sample data
In a chi-square goodness-of-fit test, what is generally used for the alternative hypothesis?
the frequency distribution does not fit the expected distribution
In a chi-square goodness-of-fit test, what is generally used for the null hypothesis?
the frequency distribution fits an expected distribution
What value does k represent when using a chi-squared test?
the number of categories
What does an r x c contingency table show?
the observed frequencies for two variables arranged in r rows and c columns with each intersection being a cell
In a chi-square independence test, what is generally used for the null hypothesis?
the variables are independent
In a chi-square independence test, what is generally used for the alternative hypothesis?
the variables are not independent
When is the f-distribution used?
to compare two variances
T/F all values of F are greater than or equal to zero
true
Define chi-square goodness-of-fit test
used to test whether a frequency distribution fits an expected distribution
In order to use the chi-squared test, each expected frequency must meet what criteria?
Ei = npi ≥ 5 each expected frequency must be at least 5
What does ANOVA stand for?
analysis of variance
Chi-square independence test, chi-square goodness-of-fit test, or both? Requires that each expected frequency is at least 5.
both
Chi-square independence test, chi-square goodness-of-fit test, or both? Requires the data be obtained from a random sample.
both
Chi-square independence test, chi-square goodness-of-fit test, or both? Testing a claim about data that are in categories.
both
What is the formula for calculating the expected frequency (E) of a category when calculating the test statistic for a chi-squared test?
n is number of trials pi is assumed probability of the i-th category
Chi-square independence test, chi-square goodness-of-fit test, or both? Degrees of freedom = k-1
chi-square goodness-of-fit test
Chi-square independence test, chi-square goodness-of-fit test, or both? Expected frequency Ei = npi
chi-square goodness-of-fit test
Chi-square independence test, chi-square goodness-of-fit test, or both? Used to test if a frequency distribution fits an expected distribution.
chi-square goodness-of-fit test
Chi-square independence test, chi-square goodness-of-fit test, or both? Degrees of freedom = (r-1)(c-1)
chi-square independence test
Chi-square independence test, chi-square goodness-of-fit test, or both? Expected frequency Er,c = ((sum row r)*(sum column c))/sample size
chi-square independence test
Chi-square independence test, chi-square goodness-of-fit test, or both? Used to test if two variables are independent.
chi-square independence test
In a two-sample F-test, how are the degrees of freedom denoted?
d.f.N = degrees of freedom of the numerator d.f.D = degrees of freedom of the denominator
In a two-sample F-test, what are the formulas for the degrees of freedom of the numerator and the degrees of freedom of the denominator?
d.f.N = n1-1 d.f.D = n2-1 where n1 and n2 are the sample sizes of the numerator and denominator respectively
