In: Statistics and Probability
A polling institute routinely conducts surveys to gauge the impact of the Internet and technology on daily life. A recent survey asked respondents if they read online journals or? blogs, an Internet activity of potential interest to many businesses. A subset of the data from this survey shows responses to this question. Test whether reading online journals or blogs is independent of generation. Use a significance level of
alpha?equals=0.05.
Read Online Journal or Blog |
||||||
?Yes, Yesterday |
?Yes, But Not Yesterday |
No |
Total |
|||
Generation |
?Gen-Y (18-30) |
2828 |
3838 |
6868 |
134134 |
|
?Gen-X (31-42) |
1313 |
3535 |
133133 |
181181 |
||
Trailing Boomers?(43-52) |
1414 |
3535 |
143143 |
192192 |
||
Leading Boomers?(53-61) |
55 |
2424 |
8686 |
115115 |
||
Matures? (62+) |
66 |
2121 |
111111 |
138138 |
||
Total |
6666 |
153153 |
541541 |
760760 |
PrintDone
Compute the chi squared ?2 test statistic.
H0: Reading online journals or blogs is independent of generation
H1: Reading online journals or blogs is not independent of generation
Let the los be alpha = 5%
The expected frequencies are
Yes, Yesterday | Yes, but not yesterday | No | Total | |
Gen Y | 6.03 | 12.718 | 14.252 | 33 |
Gen X | 17.907 | 37.767 | 42.326 | 98 |
Trailing Boomers | 7.492 | 15.8 | 17.708 | 41 |
Leading Boomers | 11.146 | 23.51 | 26.346 | 61.002 |
Maturers | 12.425 | 26.21 | 29.369 | 68.004 |
Total | 55 | 116.005 | 130.001 | 301.006 |
The chisquare contribution values are
Oi | Ei | (Oi-Ei)^2 /Ei |
6 | 6.03 | 0.0001 |
9 | 17.907 | 4.4304 |
10 | 7.492 | 0.8396 |
11 | 11.146 | 0.0019 |
19 | 12.425 | 3.4793 |
21 | 12.718 | 5.3933 |
29 | 37.767 | 2.0351 |
16 | 15.8 | 0.0025 |
20 | 23.51 | 0.524 |
30 | 26.21 | 0.548 |
6 | 14.252 | 4.778 |
60 | 42.326 | 7.3801 |
15 | 17.708 | 0.4141 |
30 | 26.346 | 0.5068 |
19 | 29.369 | 3.6609 |
Total: | 33.9941 |
Degrees of freedom: 8
Test Statistic, X^2: 33.996
Critical X^2: 15.5073
P-Value: 0.0000
Here chisquare value > Chsiquare critical value and P-value < alpha 0.05 so we reject H0
Thus ew conclude that Reading online journals or blogs is not independent of generation