Concept explainers
a.
To explain: The conditions for performing the chi-square test are met.
a.
Explanation of Solution
Given:
Goal | FEMALE | MALE |
HSC-HM | 14 | 31 |
HSC-LM | 7 | 18 |
LSC-HM | 21 | 5 |
LSC-LM | 25 | 13 |
The expected table is,
Goal | FEMALE | MALE |
HSC-HM | 22.50 | 15.50 |
HSC-LM | 12.50 | 12.50 |
LSC-HM | 13 | 13 |
LSC-LM | 19 | 22.50 |
The requirments to use chi-suare test is,
- Two categorical variables.
- Two or more categories for each variable
- Independence of observations
- Expected frequency for each cell are at least 1 or it should be at least 5 for the majority (80%) of the cells.
Since, each condition is satisfied by the given information. Therefore, chi-square test it can be used for the give dataset.
b.
To compute: The p-value of chi-square test.
b.
Answer to Problem 31E
The p-values is 0.1.621759222E-5.
Explanation of Solution
Given:
From exercise 29, the test statistics is 24.8978.
Formula used:
Calculation:
The degree of freedom for both test values, it can be calculated as
For 27 exercise,
There is the following commend to find p-value on TI83,
“
The output is,
Thus, the p-value is 0.1.621759222E-5.
c.
To explain: Give an interpretation for the p-value.
c.
Explanation of Solution
From 27, the null and alternative hypothesis,
If the null hypothesis is true, then p-value is probability of obtaining results as extreme for test statistic value.
If there is no relation between gender and sports goal, then the probability of getting a sample as extreme or more extreme as the given sample is 0.1.621759222E-5.
d.
To conclude: find the conclusion.
d.
Explanation of Solution
The null hypothesis is rejected when the p-value is less than level of significance.
Here, the p-value is less than level of significance. Thus, the null hypothesis is rejected.
Therefore, there is a sufficient evidence to conclude that there is an association between the variables goal and sex.
Chapter 11 Solutions
The Practice of Statistics for AP - 4th Edition
Additional Math Textbook Solutions
Elementary Statistics (13th Edition)
Statistics: The Art and Science of Learning from Data (4th Edition)
Statistical Reasoning for Everyday Life (5th Edition)
Elementary Statistics
Intro Stats, Books a la Carte Edition (5th Edition)
Basic Business Statistics, Student Value Edition
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