Question

According to a February 2020 Pew Research Center survey, The Virtues and Downsides of Online Dating, 30% of U.S. adults say they have used a dating site or app. The percentage is reported as 28% for Hispanics, 31% for blacks and 29% for whites. Sample sizes were reported as 663 for Hispanics, 519 for blacks, and 3,321 for whites.

At a 10% level of significance, does the survey indicate any significant difference in use of dating sites or apps among white, black, and Hispanic adults?

Answer 1

null hypothesis:Ho:

there is no differnece in use of  dating sites among white, black, and Hispanic adults

there is a differnece in use of  dating sites among white, black, and Hispanic adults

degree of freedom(df) =(rows-1)*(columns-1)=	2
for 2 df and 0.1 level , critical value       χ2=	4.605
Decision rule : reject Ho if value of test statistic X2>4.605

Applying chi square test of Homogeniety:

Expected	Ei=row total*column total/grand total	White	Black	Hispanic	Total
	Use	192.8200	150.9400	965.8600	1310
	do not use	470.1800	368.0600	2355.1400	3193
	total	663.00	519.00	3321.00	4503.00
chi square    χ2	=(Oi-Ei)2/Ei	White	Black	Hispanic	Total
	Use	0.267	0.656	0.008	0.9312
	do not use	0.110	0.2690	0.0033	0.3819
	total	0.3770	0.9249	0.0112	1.313
test statistic X2 =	1.3131

since test statistic does not falls in rejection region we fail to reject null hypothesis
we do not have have sufficient evidence to conclude that there is a difference in use of dating sites or apps among white, black, and Hispanic adults