Question

A survey described the results of a poll of working adults in Canada. Each person in a random sample was classified according to gender and the number of vacation days he or she usually took each year. The resulting data are summarized in the given table.

Days of Vacation	Gender
	Male	Female
None	51	42
1-5	21	25
6-10	67	79
11-15	108	96
16-20	71	70
21-25	82	58
More than 25	118	79

(a) Is it reasonable to conclude that there is an association between gender and the number of vacation days taken?

Test the appropriate hypotheses using a 0.05 significance level. Calculate the test statistic. (Round your answer to two decimal places.)
χ² =  

P-value interval

p < 0.001

0.001 ≤ p < 0.01  

  0.01 ≤ p < 0.05

0.05 ≤ p < 0.10

p ≥ 0.10

There is  ---Select--- enough evidence, not enough evidence to conclude that there is an association between gender and the number of vacation days taken.

(b) To what population would it be reasonable to generalize this conclusion?

all working adults

all adults    

only male working adults

only female working adults

working adults in Canada

Answer 1

a)

Chi square test of independence is used to test the association between gender and number of vacation.

The Chi-Square Value is obtained using the formula

Where, the observed values are,

Days of Vacation	Gender
	Male	Female	Total
None	51	42	93
1--5	21	25	46
6--10	67	79	146
11--15	108	96	204
16--20	71	70	141
21--25	82	58	140
More than 25	118	79	197
Total	518	449	967

and the expected values are obtained using the formula,

Days of Vacation	Gender
	Male	Female	Total
None			93
1--5	24.64	21.36	46
6--10	78.21	67.79	146
11--15	109.28	94.72	204
16--20	75.53	65.47	141
21--25	74.99	65.01	140
More than 25	105.53	91.47	197
Total	518	449	967

Now, the chi-square value is obtained as follow,

Observed,	Expected,
51	49.82	1.18	1.40	0.03
21	24.64	-3.64	13.26	0.54
67	78.21	-11.21	125.64	1.61
108	109.28	-1.28	1.63	0.01
71	75.53	-4.53	20.53	0.27
82	74.99	7.01	49.07	0.65
118	105.53	12.47	155.54	1.47
42	43.18	-1.18	1.40	0.03
25	21.36	3.64	13.26	0.62
79	67.79	11.21	125.64	1.85
96	94.72	1.28	1.63	0.02
70	65.47	4.53	20.53	0.31
58	65.01	-7.01	49.07	0.75
79	91.47	-12.47	155.54	1.70
			Sum	9.88

The P-value is obtained from ch square distribution table for degree of freedom = (r-1)(c-1) = (7-1)(2-1)=6

Since the P-value is greater than 0.05 at 5% significance level, the null hypothesis is not rejected.

There is not enough evidence to conclude that there is an association between gender and the number of vacation days taken

b)

(b)

Answer: working adults in Canada

Explanation: Since the hypothesis test is performed for working professional of Canada, hence only population of Canada would be reasonable to generalize this conclusion