Question 1

In testing the difference between two population proportions, we pool the two sample proportions to estimate the population proportion.

Accepted Answer

Yes, we pool the sample proportions to estimate the population proportion when conducting inference about the difference between two proportions. This is done under the assumption that the two populations have equal proportions for the variable being studied.

Question 2

The variance of the chi-square distribution is equal to one.

Accepted Answer

The variance of the chi-square distribution is equal to twice the degrees of freedom, not one.

Question 3

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 the normality of a sample, we typically use statistical tests such as the Shapiro-Wilk test, Kolmogorov-Smirnov test, or Anderson-Darling test. These tests compare the observed distribution of the data to a theoretical normal distribution, and if the p-value is greater than our level of significance (usually 0.05), we fail to reject the null hypothesis that the data is normally distributed.

Question 4

The chi-square distribution is positively skewed.

Accepted Answer

The chi-square distribution is a continuous probability distribution that is positively skewed, meaning that the tail of the distribution extends to the right. This is because the distribution is bounded below by zero but has no upper bound, so extreme values are more likely to occur on the right side of the distribution.

Question 5

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

Accepted Answer

Nonparametric tests do not require any assumptions about the population distribution, making them useful in situations where the underlying distribution is unknown or non-normal.

Question 6

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

Accepted Answer

The shape of the chi-square distribution changes with the number of degrees of freedom. For smaller degrees of freedom, the distribution is skewed and long-tailed, while at higher degrees of freedom, it becomes more normal in shape.

Question 7

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

Accepted Answer

This statement is true. The chi-square test statistic used in a goodness-of-fit test has k - 1 degrees of freedom, where k is the number of categories or groups being compared.

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

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

The chi-square distribution is commonly used in goodness-of-fit tests to determine if there is a significant difference between the observed and expected distributions.

Question 10

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

Accepted Answer

The answer of The use of the chi-square statistic would...

Question 11

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 statement is true, as the chi-square distribution varies based on the degrees of freedom. Each different number of degrees of freedom results in a different chi-square distribution.

Question 12

Some important uses of the chi-square include testing for the association of two categorical variables.

Accepted Answer

The chi-square test is commonly used to test for the association between two categorical variables. It can also be used for other purposes such as testing for goodness of fit and independence of proportions.

Question 13

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 dividing the row total multiplied by the column total by the grand total.

Question 14

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 15

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

Accepted Answer

A t-statistic is used to test a hypothesis about a population mean when the population standard deviation is unknown. It is not used to compute an expected normal distribution.

Question 16

If we are testing the difference between two population proportions, it is assumed that the two populations are approximately normal and have equal variances.

Accepted Answer

When testing the difference between two population proportions, the assumption is that the sample sizes are large enough to satisfy the Central Limit Theorem, rather than assuming that the populations are approximately normal. Additionally, the assumption of equal variances is typically only made when testing the difference between two population means, not proportions.

Question 17

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

A chi-square null hypothesis typically states that there is no association between the variables being studied, so the correct null hypothesis in this context would assert that there is no difference in parking lot preference between male and female students at Coastal Carolina University.

Question 18

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

H₀ represents the null hypothesis that sales are uniformly distributed among the five locations, while H₁ represents the alternate hypothesis that sales are not uniformly distributed among the five locations. Therefore, the statement is true.

Question 19

The pooled estimate of the proportion is found by dividing the total number of samples by the total number of successes.

Accepted Answer

The pooled estimate of the proportion is found by dividing the total number of successes by the total number of samples.

Question 20

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...

Quiz 15: Nonparametric Methods: Nominal Level Hypothesis Tests