Question

Does gender influence the satisfaction reported by library patrons?

(a) " 18 women and 14 men reported that they were not satisfied with the library service.

(b) " 33 women and 20 men reported that they were satisfied.

(c) " 57 women and 85 men reported that they were very satisfied with the service.

Answer 1

Here, we can use the chi-square test of association and our hypothesis is,

H0: The gender and satisfaction level are independent.

Vs., H1: The gender and satisfaction level are not independent.

The observed frequencies are,

	Women	Men	Total
not satisfied	18	14	32
Satisfied	33	20	53
very satisfied	57	85	142
Total	108	119	227

and expected frequency of a cell is given by, (row total* Column total)/ Grand total

And the table of expected frequency is,

	Women	Men	Total
not satisfied	15.22	16.78	32
Satisfied	25.22	27.78	53
very satisfied	67.56	74.44	142
Total	108	119	227

and the test statistic is,

= 0.506+2.403+1.65+0.459+2.181+1.498=8.697

df=(r-1)(c-1)=2

th chi-square tabulated value at 0.05 level of significance is, 5.991.

Since our test statistic is greater than the tabulated value, we reject the null hypothesis.

There is enough evidence to conclude that gender influence the satisfaction reported by library patrons