a.
To show: The provided data in a two-way table and conduct an appropriate chi-square test. Also, summarize the obtained results.
a.
Answer to Problem 6CRE
There is insufficient evidence to support the claim of association.
Explanation of Solution
Given:
Number of consumers = 120
Number of students that said Yes = 22
Number of students that said No = 68
Formula used:
The formula to compute the chi-square test statistic is:
Calculation:
Using the provided information, the table is constructed as:
Yes | No | Total | |
Student | 22 | 39 | 61 |
Non-student | 30 | 29 | 59 |
Total | 52 | 68 | 120 |
Using this table, the expected frequencies are:
Yes | No | Total | |
Student | 26.4333 | 34.5667 | 61 |
Non-student | 25.5667 | 33.4333 | 59 |
Total | 52 | 68 | 120 |
The hypotheses are:
The chi-square test statistic could be calculated as:
The degree of freedom is:
The p-value using chi-square table at 6 degree of freedom is 0.102
The p-value is above significance level. The null hypothesis does not get rejected. There is enough evidence to be in favor of claim at 5% significance level.
b.
To analyze: The results of above part using the z-method. Also, check if the chi-square test statistic is the square of z-statistic.
b.
Answer to Problem 6CRE
The chi-square test statistic is the square of z-statistic.
Explanation of Solution
Calculation:
The null and alternative hypotheses are:
The proportion of students and non-students are:
The output obtained using the Ti-83 plus calculator is:
From the above output, the p-value is 0.1023.
The p-value is above significance level. The null hypothesis could not be rejected. There is not enough evidence to conclude that there is a difference in two population proportions at 5% significance level.
Now, the verification for the chi-square test statistic could be done as:
Here, z-test statistic is -1.634.
Take square of z- statistic as:
Here, obtained value is same as the chi-square test statistic. Thus, it could be said that the chi-square test statistic is the square of z-statistic.
Chapter 11 Solutions
The Practice of Statistics for AP - 4th Edition
Additional Math Textbook Solutions
Statistical Reasoning for Everyday Life (5th Edition)
An Introduction to Mathematical Statistics and Its Applications (6th Edition)
Introductory Statistics (2nd Edition)
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Statistics: The Art and Science of Learning from Data (4th Edition)
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