Chapter 11.2, Problem 43E

To determine

To perform hypothesis testing.

Answer to Problem 43E

There is no convincing evidence that there is an association between relative finger length and gender in the population of students who completed the survey.

Explanation of Solution

Given:

		Gender
		Female	Male
Relative finger length	Index longer	85	73
	Same length	42	44
	Ring longer	100	116

The null and alternative hypotheses:

  $H_0$ : There is no association between relative finger length and gender.

  $H_a$ : There is association between relative finger length and gender.

Using excel,

		Female	Male	Total
Index longer	Observed	85	73	158
	Expected	77.97	80.03	158.00
	(O - E)² / E	0.63	0.62	1.25
Same length	Observed	42	44	86
	Expected	42.44	43.56	86.00
	(O - E)² / E	0.00	0.00	0.01
Ring longer	Observed	100	116	216
	Expected	106.59	109.41	216.00
	(O - E)² / E	0.41	0.40	0.80
Total	Observed	227	233	460
	Expected	227.00	233.00	460.00
	(O - E)² / E	1.05	1.02	2.07
		2.07	chi-square
		2	df
		.3561	p-value

Chi-square test statistic = 2.07. The degrees of freedom = 2 and p-value = 0.3561.

Decision: P-value > 0.05, fail to reject H0.

Conclusion: There is no convincing evidence that there is an association between relative finger length and gender in the population of students who completed the survey.