Question 1

Which of the following is recorded using a chi-square goodness-of-fit test and a chi-square test for independence?

Accepted Answer

Both chi-square goodness-of-fit test and chi-square test for independence involve comparing the observed frequencies to the expected frequencies. Therefore, both frequency observed and frequency expected are recorded using these tests.

Question 2

A researcher records the frequency of participants selecting one of four new slogans for an advertising campaign.If it was expected that among 200 people polled there would be no preference for any one slogan,then what was the expected frequency for each slogan.

Accepted Answer

If there is no preference for any one slogan, then each slogan would be selected roughly an equal number of times. Therefore, we can divide the number of people polled (200) by the number of slogans (4) to determine the expected frequency for each slogan:

200/4 = 50

So the expected frequency for each slogan is 50 people.

Question 3

Which of the following is an example of a parametric test?

Accepted Answer

All of the options listed (analysis of variance, one-sample t test, Pearson correlation) are examples of parametric tests, which are statistical tests that assume the underlying data distributions are known and can be characterized by parameters such as the mean and variance.

Question 4

Many nonparametric tests are called ______ because they make no assumptions regarding the shape of the distribution in the population.

Accepted Answer

Nonparametric tests are also called distribution-free tests because they do not rely on any assumptions about the specific distribution of data in the population. Parametric tests, on the other hand, make assumptions about the underlying population distribution (such as normality) in order to calculate statistical significance. Therefore, nonparametric tests are useful when dealing with non-normally distributed data or small sample sizes where the assumption of normality may not be valid.

Question 5

A researcher asks participants to taste each of three meals and to choose the one they like best.The same foods are in each meal,expect for the calorie total of the meal (which is low,moderate,or high calorie).Based on the observed frequencies given below,what is an appropriate conclusion for this test at a .05 level of significance?

Accepted Answer

The answer of A researcher asks participants to taste each...

Question 6

A researcher conducts a chi-square goodness-of-fit test in which k = 2 and $\chi$² = 3.98.What is the decision for this test at a .05 level of significance?

Accepted Answer

For a chi-square goodness-of-fit test with k = 2, the critical value at a .05 level of significance is 3.84. Since the calculated chi-square value of 3.98 is greater than the critical value, we reject the null hypothesis.

Question 7

Which of the following is an example of a nonparametric test?

Accepted Answer

The chi-square test is a nonparametric test that is often used to analyze categorical or nominal data. The other options (A, B, and D) are all examples of parametric tests, which require certain assumptions to be met about the data's underlying distribution.

Question 8

A researcher selects a sample of 80 people and records the frequency of participants choosing a low,moderate,or high calorie dessert in a buffet.What are the degrees of freedom for this chi-square goodness-of-fit test?

Accepted Answer

The degrees of freedom for a chi-square goodness-of-fit test are calculated as the number of categories minus one. In this case, there are three categories (low, moderate, or high calorie dessert), so the degrees of freedom are 3 - 1 = 2.

Question 9

A local ice cream shop wants to see if they should promote a new swizzleberry swirl or creamsicle flavored drink.In order to determine which one to promote,they took a sample of 80 patrons and asked them to choose which they preferred.The one that is significantly preferred over the other (at a .05 level of significance)will be promoted.It is expected that an equal number of patrons will choose each flavor.Based on the observed frequencies given below,what is the decision for this test?

Accepted Answer

The answer of A local ice cream shop wants to...

Question 10

A chi-square goodness-of-fit test shows that the frequencies observed equal those that were expected.Hence,the value of the test statistic is ______.

Accepted Answer

When the observed frequencies equal the expected frequencies, it means there is no significant difference between the observed and expected values. Therefore, the value of the test statistic is 0.

Question 11

As a general rule,the larger the degrees of freedom for a chi-square test,______.

Accepted Answer

The critical value for a chi-square test increases as the degrees of freedom increase. This is because as the sample size increases (and degrees of freedom increase), the distribution becomes less spread out and more normal. As a result, we need a larger critical value to reject the null hypothesis and achieve the same level of significance.

Question 12

A researcher compares the frequency of participants who sleep primarily on their stomach,back,or side during the night.What is the critical value for a chi-square goodness-of-fit test at a .05 level of significance?

Accepted Answer

The critical value for a chi-square goodness-of-fit test with 2 degrees of freedom (3 categories - 1) at a .05 level of significance is 5.99.

Question 13

What is a key distinction between parametric tests and nonparametric tests in terms of scales of measurement?

Accepted Answer

A key distinction between parametric tests and nonparametric tests is that parametric tests are used for interval and ratio data, while nonparametric tests are used for nominal and ordinal data. This is because parametric tests assume that the data follows a normal distribution and have specific requirements for the data, such as equal variances, which are not necessary for nonparametric tests. Nonparametric tests are also more robust to outliers and non-normal data distributions.

Question 14

A researcher conducts a chi-square goodness-of-fit test in which k = 5.What is the critical value for this test at a .05 level of significance?

Accepted Answer

The critical value for a chi-square goodness-of-fit test with k = 5 at a .05 level of significance is 9.49, according to a chi-square distribution table.

Question 15

To appropriately interpret the chi-square goodness-of-fit test,it is necessary to compare differences ______.

Accepted Answer

The chi-square goodness-of-fit test compares the observed frequencies of a categorical variable to the expected frequencies under the null hypothesis. To appropriately interpret the test, it is necessary to compare the differences between the observed and expected frequencies at each level of the categorical variable.

Question 16

A researcher conducts a chi-square goodness-of-fit test in which k = 3 and $\chi$10² = 4.32.What is the decision for this test at a .05 level of significance?

Accepted Answer

The critical value for a chi-square test with 2 degrees of freedom (k-1) at a 0.05 significance level is approximately 5.99. Since 4.32 is less than 5.99, we retain the null hypothesis.

Question 17

A chi-square goodness-of-fit test shows that the frequencies observed fit well with those that were expected.Hence,the decision was to ______.

Accepted Answer

Since the frequencies observed fit well with those that were expected, there is no evidence to suggest that there is a significant difference between the observed and expected frequencies. Therefore, we can retain the null hypothesis, which states that there is no significant difference between the observed and expected frequencies.

Question 18

The degrees of freedom for a chi-square goodness-of-fit test are ______.

Accepted Answer

The degrees of freedom for a chi-square goodness-of-fit test are equal to the number of categories minus 1, which is given by k - 1.

Question 19

We compute the frequency expected in each category using known ______ stated in the null hypothesis.

Accepted Answer

When testing a hypothesis about proportions, we use the null hypothesis to determine the expected proportions in each category. Therefore, the correct choice is B, proportions.

Question 20

Which of the following is a statistical procedure used to test hypotheses about the discrepancy between the observed and expected frequencies in two or more nominal categories?

Accepted Answer

The chi-square test is specifically designed to test the null hypothesis that there is no significant difference between the observed and expected frequencies in two or more nominal categories. One-way ANOVA and analysis of regression are not designed for this purpose.

Quiz 17: Nonparametric Tests: Chi-Square Tests

Which of the following is recorded using a chi-square goodness-of-fit test and a chi-square test for independence?

A researcher records the frequency of participants selecting one of four new slogans for an advertising campaign.If it was expected that among 200 people polled there would be no preference for any one slogan,then what was the expected frequency for each slogan.

Which of the following is an example of a parametric test?

Many nonparametric tests are called ______ because they make no assumptions regarding the shape of the distribution in the population.

A researcher conducts a chi-square goodness-of-fit test in which k = 2 and $\chi$ ² = 3.98.What is the decision for this test at a .05 level of significance?

Which of the following is an example of a nonparametric test?

A researcher selects a sample of 80 people and records the frequency of participants choosing a low,moderate,or high calorie dessert in a buffet.What are the degrees of freedom for this chi-square goodness-of-fit test?

A chi-square goodness-of-fit test shows that the frequencies observed equal those that were expected.Hence,the value of the test statistic is ______.

As a general rule,the larger the degrees of freedom for a chi-square test,______.

A researcher compares the frequency of participants who sleep primarily on their stomach,back,or side during the night.What is the critical value for a chi-square goodness-of-fit test at a .05 level of significance?

What is a key distinction between parametric tests and nonparametric tests in terms of scales of measurement?

A researcher conducts a chi-square goodness-of-fit test in which k = 5.What is the critical value for this test at a .05 level of significance?

To appropriately interpret the chi-square goodness-of-fit test,it is necessary to compare differences ______.

A researcher conducts a chi-square goodness-of-fit test in which k = 3 and $\chi$ 10² = 4.32.What is the decision for this test at a .05 level of significance?

A chi-square goodness-of-fit test shows that the frequencies observed fit well with those that were expected.Hence,the decision was to ______.

The degrees of freedom for a chi-square goodness-of-fit test are ______.

We compute the frequency expected in each category using known ______ stated in the null hypothesis.

Which of the following is a statistical procedure used to test hypotheses about the discrepancy between the observed and expected frequencies in two or more nominal categories?

Quiz 17: Nonparametric Tests: Chi-Square Tests

Which of the following is recorded using a chi-square goodness-of-fit test and a chi-square test for independence?

A researcher records the frequency of participants selecting one of four new slogans for an advertising campaign.If it was expected that among 200 people polled there would be no preference for any one slogan,then what was the expected frequency for each slogan.

Which of the following is an example of a parametric test?

Many nonparametric tests are called ______ because they make no assumptions regarding the shape of the distribution in the population.

A researcher conducts a chi-square goodness-of-fit test in which k = 2 and χ\chiχ 2 = 3.98.What is the decision for this test at a .05 level of significance?

Which of the following is an example of a nonparametric test?

A researcher selects a sample of 80 people and records the frequency of participants choosing a low,moderate,or high calorie dessert in a buffet.What are the degrees of freedom for this chi-square goodness-of-fit test?

A chi-square goodness-of-fit test shows that the frequencies observed equal those that were expected.Hence,the value of the test statistic is ______.

As a general rule,the larger the degrees of freedom for a chi-square test,______.

A researcher compares the frequency of participants who sleep primarily on their stomach,back,or side during the night.What is the critical value for a chi-square goodness-of-fit test at a .05 level of significance?

What is a key distinction between parametric tests and nonparametric tests in terms of scales of measurement?

A researcher conducts a chi-square goodness-of-fit test in which k = 5.What is the critical value for this test at a .05 level of significance?

To appropriately interpret the chi-square goodness-of-fit test,it is necessary to compare differences ______.

A researcher conducts a chi-square goodness-of-fit test in which k = 3 and χ\chiχ 102 = 4.32.What is the decision for this test at a .05 level of significance?

A chi-square goodness-of-fit test shows that the frequencies observed fit well with those that were expected.Hence,the decision was to ______.

The degrees of freedom for a chi-square goodness-of-fit test are ______.

We compute the frequency expected in each category using known ______ stated in the null hypothesis.

Which of the following is a statistical procedure used to test hypotheses about the discrepancy between the observed and expected frequencies in two or more nominal categories?

A researcher conducts a chi-square goodness-of-fit test in which k = 2 and $\chi$ ² = 3.98.What is the decision for this test at a .05 level of significance?

A researcher conducts a chi-square goodness-of-fit test in which k = 3 and $\chi$ 10² = 4.32.What is the decision for this test at a .05 level of significance?