Question 1

The use of the chi-square statistic would be permissible in the following goodness-of-fit test.

Accepted Answer

False

Question 2

To test the null hypothesis that a set of sample data is normally distributed, we compare an expected normal distribution of the data to an observed distribution of the data.

Accepted Answer

To test if a set of sample data is normally distributed, we use statistical tests such as the Shapiro-Wilk test and compare the observed distribution to a normal distribution using graphical methods such as a normal probability plot.

Question 3

The shape of the chi-square distribution depends on the size of the sample.

Accepted Answer

The shape of the chi-square distribution depends on the degrees of freedom, not directly on the size of the sample.

Question 4

The null hypothesis in the goodness-of-fit test is __________.

Accepted Answer

The answer of The null hypothesis in the goodness-of-fit test...

Question 5

Nonparametric tests require no assumptions about the shape of the population distribution.

Accepted Answer

Nonparametric tests do not require assumptions about the shape of the population distribution.

Question 6

The claim that "male and female students at Coastal Carolina University prefer different parking lots on campus" is an example of a chi-square null hypothesis.

Accepted Answer

The claim actually represents an alternative hypothesis because it suggests a specific relationship or difference between groups (male and female students) in their preferences for parking lots, which is something you would test against a null hypothesis that assumes no difference in preferences.

Question 7

As the degrees of freedom increase, the shape of a chi-square distribution approaches a ______________ distribution.

Accepted Answer

The answer of As the degrees of freedom increase, the...

Question 8

The computed value of a chi-square statistic is always positive because the numerator is the difference between the observed frequencies and the expected frequencies ______________.

Accepted Answer

The answer of The computed value of a chi-square statistic...

Question 9

A scatter plot is a useful graphical method to determine if a set of sample data is from a normal population.

Accepted Answer

A scatter plot can show the relationship between two variables, but it cannot determine if the data is from a normal population. Statistical tests, such as Shapiro-Wilk or Kolmogorov-Smirnov, should be used to assess normality.

Question 10

For a goodness-of-fit test, the following are possible null and alternate hypotheses: H₀: Sales are uniformly distributed among the five locations. H₁: Sales are not uniformly distributed among the five locations.

Accepted Answer

These are possible null and alternate hypotheses for a goodness-of-fit test to determine if sales are uniformly distributed among five locations. The null hypothesis states that sales are uniformly distributed, while the alternate hypothesis states that sales are not uniformly distributed.

Question 11

The chi-square distribution is positively skewed.

Accepted Answer

The chi-square distribution is skewed to the right or positively skewed. It is not symmetric. The skewness increases as the degrees of freedom decrease.

Question 12

For a contingency table, the expected frequency for a cell is found by dividing the row total by the grand total.

Accepted Answer

The expected frequency for a cell is found by multiplying the row total and column total and then dividing by the grand total.

Question 13

A t-statistic is useful for computing an expected normal distribution.

Accepted Answer

A t-statistic is used to test the significance of the difference between two sample means and does not directly compute an expected normal distribution.

Question 14

An F distribution is useful for testing the null hypothesis that a set of sample data is normally distributed.

Accepted Answer

An F distribution is actually used for testing the equality of variances of two populations or groups. It is not directly used for testing normality of data. However, there are certain tests that use the F distribution as a part of their calculation that can indirectly test for normality, such as the Shapiro-Wilk test.

Question 15

The shape of the chi-square distribution depends on the number of degrees of freedom.

Accepted Answer

The shape of the chi-square distribution does depend on the number of degrees of freedom. This distribution becomes more symmetric and bell-shaped as the degrees of freedom increase.

Question 16

A chi-square goodness-of-fit test is used to determine how well an observed distribution fits an _________ distribution.

Accepted Answer

The answer of A chi-square goodness-of-fit test is used to...

Question 17

The chi-square test statistic used in a goodness-of-fit test has k - 1 degrees of freedom.

Accepted Answer

This is correct. The number of degrees of freedom for a goodness-of-fit chi-square test is k - 1, where k is the number of categories or groups being compared.

Question 18

There is not one, but a family of chi-square distributions. There is a chi-square distribution for 1 degree of freedom, another for 2 degrees of freedom, another for 3 degrees of freedom, and so on.

Accepted Answer

This is correct, there are different chi-square distributions for different degrees of freedom.

Question 19

The lowest level of measurement for a chi-square goodness-of-fit test is the ______________ level.

Accepted Answer

The answer of The lowest level of measurement for a...

Question 20

In the goodness-of-fit test, the chi-square distribution is used to determine how well an observed distribution of observations "fits" an expected distribution of observations.

Accepted Answer

This is a correct statement about the goodness-of-fit test.

Quiz 15: Nonparametric Methods: Goodness-Of-Fit Tests