QUESTIONS
Question 1
You are conducting a multinomial hypothesis test for the claim that all 5 categories are equally likely to be selected. Complete the table.
| Category | Observed Frequency | Expected Frequency | Squared Pearson Residual |
| A | 11 | ||
| B | 11 | ||
| C | 5 | ||
| D | 14 | ||
| E | 15 |
What is the chi-square test-statistic for this data?
X2 =
Report all answers accurate to three decimal places.
Question 2
You are conducting a multinomial hypothesis test for the claim that the 4 categories occur with the following frequencies:
H0 : PA = 0.15; PB = 0.15; PC = 0.3; PD = 0.4.
Complete the table:
| Category | Observed Frequency | Expected Frequency | Squared Residual |
| A | 43 | ||
| B | 40 | ||
| C | 42 | ||
| D | 64 |
What is the chi-square test-statistic for this data?
X2 =
Report all answers accurate to three decimal places.
Question 3
You intend to conduct a goodness-of-fit test for a multinomial distribution with 3 categories. You collect data from 67 subjects.
What are the degrees of freedom for the X2 distribution for this test?
d.f. =
Question 4
You are conducting a multinomial Goodness of Fit hypothesis test for the claim that all 5 categories are equally likely to be selected. Complete the table. Report all answers correct to three decimal places.
| Category | Observed Frequency | Expected Frequency | Pearson Residual |
| A | 8 | ||
| B | 9 | ||
| C | 11 | ||
| D | 6 | ||
| E | 15 |
What is the chi-square test-statistic for this data?
X2 =
For significance level alpha 0.05, what is the chi-square Critical value?
Critical Value =
What would be the conclusion of this hypothesis test?
- Fail to reject the Null Hypothesis.
- Reject the Null Hypothesis.
Question 5
You are conducting a multinomial Goodness of Fit hypothesis test for the claim that the 4 categories occur with the following frequencies:
H0: PA = 0.4; PB = 0.15; PC = 0.3; PD = 0.15.
Complete the table. Report all answers accurate to three decimal places.
| Category | Observed Frequency | Expected Frequency | Residual |
| A | 50 | ||
| B | 16 | ||
| C | 37 | ||
| D | 18 |
What is the chi-square test-statistic for this data?
X2 =
For significance level alpha 0.05, what is the chi-square Critical Value?
Critical Value =
What would be the conclusion of this hypothesis test?
- Fail to reject the Null Hypothesis
- Reject the Null Hypothesis.
Question 6
The National Longitudinal Study of Adolescent Health interviewed several thousand teens (grades 7 to 12). One question asked was “What do you think are the chances you will be married in the next 10 years?” Here is a two-way table of the responses by gender:
| Opinion | Female | Male |
| Almost no chance | 114 | 99 |
| Some chance but probably not | 136 | 158 |
| A 50-50 chance | 441 | 517 |
| A good chance | 725 | 726 |
| Almost Certain | 1166 | 772 |
- How many individuals are described in this table?
How many females were among the respondents?
Answer =
- The percent of females among the respondents was about ______%.
Your percent from the previous exercise is part of
- The marginal distribution of opinion about marriage
- The Marginal distribution of sex
- The conditional distribution of sex among adolescents with given opinion
What percent of females thought that they were almost certain to be married in the next 10 years?
Answer = 45.16
Your percent from the previous exercise is part of
- The conditional distribution of sex among those who thought they were almost certain to be married.
- The marginal distribution of opinion about marriage
- The Conditional distribution of opinion about marriage among women
Question 7
At the beginning of the semester we collected some data from you. Two of the questions on the survey were about gender and whether or not you have equal, more, or less energy in the afternoon compared to the morning. Below are the results.
| Equal | Less | More | |
| Female | 18 | 37 | 24 |
| Male | 9 | 15 | 23 |
Assuming that gender and energy levels are not associated, what is the expected value for the number of males who have equal energy in the afternoon as the morning?
Answer =
Question 8
At a stop sign, some drivers come to a full stop, some come to a `rolling stop’ (not a full stop, but slow down), and some do not stop at all. We would like to test if there is an association between gender and type of stop (full, rolling, or no stop). We collect data by standing a few feet from a stop sign and taking note of type of stop and the gender of the driver. What are the hypotheses for testing for an association between gender and type of stop?
- H0: Males and females are equally likely to come to a full stop. HA: Males and females are not equally likely to come to a full stop.
- H0: Gender and type of stop are associated. HA: Gender and type of stop are independent.
- H0: Gender and type of stop are independent. HA: Gender and type of stop are associated
- H0: Males and females are equally likely to come to a rolling stop. HA: Males are more likely than females to come to a rolling stop.
ANSWERS
Question 1
You are conducting a multinomial hypothesis test for the claim that all 5 categories are equally likely to be selected. Complete the table.
| Category | Observed Frequency | Expected Frequency | Squared Pearson Residual |
| A | 11 | ||
| B | 11 | ||
| C | 5 | ||
| D | 14 | ||
| E | 15 |
What is the chi-square test-statistic for this data?
X2 =
Report all answers accurate to three decimal places.