Question

2. Suppose that you wanted to examine racial differences in social media use. You hypothesize black people are more likely to use Twitter than white people. Rather than administer your own survey, you use the already-existing General Social Survey and find the following frequencies:

​White​Black

​Use Twitter​186​47

​Don’t​856​159​

a) To facilitate comparison (and account for the fact that there are more white people than black people in the U.S.), convert the frequencies in the table above to percentages. Round to one place after the decimal. Create a new table below.

b) Identify the main relationship that your table from “a” depicts (using only words, no numbers).

c) Use the chi-square calculator linked in the slides to generate a p-value for this data. (Important: use the frequencies from the original table, not the percentages from “a”)

d) Is the difference between white and black respondents statistically significant?

e) To write up this result, write a paragraph below with the following structure:

1. First sentence should sum up the main relationship (answer to “b”)

2. Report the percentages that describe the main relationship (not all of them). Round to the nearest whole number.

3. Identify whether the relationship is significant (answer to “d”)

4. Identify whether or not the hypothesis has been supported.

Answer 1

(a) The table is:

		White	Black	Total
Use Twitter	% of total	14.9%	3.8%	18.7%
Don't	% of total	68.6%	12.7%	81.3%
Total	% of total	83.5%	16.5%	100.0%

(b) There is a strong relationship between whites who don't use twitter.

(c) The p-value is 0.0947.

		White	Black	Total
Use Twitter	Observed	186	47	233
	Expected	194.54	38.46	233.00
	O - E	-8.54	8.54	0.00
	(O - E)² / E	0.37	1.90	2.27
Don't	Observed	856	159	1015
	Expected	847.46	167.54	1015.00
	O - E	8.54	-8.54	0.00
	(O - E)² / E	0.09	0.44	0.52
Total	Observed	1042	206	1248
	Expected	1042.00	206.00	1248.00
	O - E	0.00	0.00	0.00
	(O - E)² / E	0.46	2.33	2.79
		2.79	chi-square
		1	df
		.0947	p-value

(d) The difference between white and black respondents is not statistically significant.

(e) The hypothesis being tested is:

H₀: There is no relationship between white and black respondents

H_a: There is a relationship between white and black respondents

The chi-square test statistic is 2.79.

The p-value is 0.0947.

Since the p-value (0.0947) is greater than the significance level (0.05), we fail to reject the null hypothesis.

Therefore, we cannot conclude that there is a relationship between white and black respondents.