Q.90 Use a solution sheet to solve th... [FREE SOLUTION]

91影视

Introductory Statistics

Barbara Illowsky, Susan Dean

$Math Studyset 91影视 Explanations$ Math

OER 2018 Edition 路 902 pages

ISBN: 9781938168208

Chapter 11: Q.90 (page 664)

Use a solution sheet to solve the hypothesis test problem. Go to Appendix E for the chi-square solution sheet. Round expected frequency to two decimal places.
A manager of a sports club keeps information concerning the main sport in which members participate and their ages. To test whether there is a relationship between the age of a member and his or her choice of sport, $643$ members of the sports club are randomly selected. Conduct a test of independence.
Sport $18 - 25$ $26 - 30$ $31 - 40$ $41 a n d o v e r$
racquetball $42$ $58$ $30$ $46$
tennis $58$ $76$ $38$ $65$
swimming $72$ $60$ $65$ $33$

Short Answer

Expert verified

H₀ : There is no significant association between the age of a member and his or her choice of sport.

Decision: The computed value of the chi-square test statistic is greater than the critical value, so the null hypothesis will be rejected at a $5$ % level of significance.

Conclusion: There is sufficiently proof at a $5$ % level of significance to conclude that there is a significant collaboration between the age of a member and his or her choice of sport.

Step by step solution

Given Information

To test whether there is a relationship between the age of a member and his or her choice of sport, $643$ members of the sports club are randomly selected. Conduct a test of independence.

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Face Value	Frequency	Expected Frequency
1	15
2	29
3	16
4	15
5	30
6	15

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Sport	$18 - 25$	$26 - 30$	$31 - 40$	$41 a n d o v e r$
racquetball	$42$	$58$	$30$	$46$
tennis	$58$	$76$	$38$	$65$
swimming	$72$	$60$	$65$	$33$