a.
To explain: The null and alternative hypotheses for a significance test.
a.
Explanation of Solution
Given:
The observed value ( Oi ) is:
Goal | FEMALE | MALE |
HSC-HM | 14 | 31 |
HSC-LM | 7 | 18 |
LSC-HM | 21 | 5 |
LSC-LM | 25 | 13 |
Calculation:
To test whether there is a difference of sports goals for male and female undergraduates at the university or not.
The null and alternative hypotheses are:
b.
To find: The expected counts for the given data set.
b.
Explanation of Solution
Formula used:
The
Calculation:
From the given table,
Goal | FEMALE | MALE | Total |
HSC-HM | 14 | 31 | 45 |
HSC-LM | 7 | 18 | 25 |
LSC-HM | 21 | 5 | 26 |
LSC-LM | 25 | 13 | 38 |
Total | 67 | 67 | 134 |
The expected value ( Ei ), can be calculated as:
Goal | FEMALE | MALE |
HSC-HM | ||
HSC-LM | ||
LSC-HM | ||
LSC-LM |
c.
To find: The chi-square statistic.
c.
Answer to Problem 29E
The chi-square test value, is 24.8978.
Explanation of Solution
Formula used:
The chi-square test statistics value:
Calculation:
The chi-square statistic, can be calculated as:
Thus, the chi-square test value, is 24.8978.
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