Sample analysis
Chapter 9
Question 11.29
- The chi-square test of independence can be used only if the following conditions are met:
| • To begin with, the study should have employed a simple random sampling method to select the samples for the study. | • Secondly, since the test compares two variables from two samples, the variables should be categorical in nature. | • Lastly, the sample size should be large. Since the data is mostly presented on a contingency table, the frequency count for each cell should not be below 5. | |
| Question 11.31 | |||
| Since we have four activities, we will have four different frequency tables. | a. Played a game on a video game system | Contingency Table | |
| Played a video game Yes No Total | Boys 498 102 600 | Girls 243 380 623 Total 741 482 1223 |
The null hypothesis is that there is no difference between girls and boys playing a game on a video game system.
Expected Table
| P | layed a video game yes no Total | ||
| Boys (600*741)/1223=363.5 (600*482)/1223=236.7 600 | Girls (623*741)/1223=377.5 (623*482)/1223=245.5 623 | ||
| Total | 741 482 1223 |
X2= (
With a significance level of 0.05 and 1 degree of freedom, the Chi-square distribution table results in a value of 3.84.
The degrees of freedom is calculated as (2-1)(2-1)= 1
498-363.5)2/363.5+(102-236.7)2/236.7+(243-377.5)2/377.5+(380-245.5)2/245.5= 49.7+76.5+47.9+73.64= 247.7
Since 247.7>3.84, we reject the null hypothesis, and thus confirm that there is indeed a difference between boys and girls playing video games.
- Read a book for fun
Contingency Table
- Read a book for fun Yes No Total
- Boys 276 324 600
- Girls 324 299 623
- Total 600 623 1223
- Expected Table
- Read a book for fun Yes No Total
- Boys (600*600)/1223= 294.4 (600*623)/1223= 305.6 600
- Girls (623*600)/1223= 305.6 (623*623)/1223= 317.4 623
- Total 600 623 1223
- X2= (276-294.4)2/294.4+(324-305.6)2/305.6+(324-305.6)2/305.6+(299-317.4)2/317.4= 1.15+1.11+1.11+1.07= 4.44
- Since 4.44>3.84, there is a difference between the proportion
| of boys and girls who read a book for fun. c. Gave advice product for parents Contingency Table
| Gave advice Yes No | Total | ||
| Boys 186 414 600 | ||||
| Girls 181 442 623 | ||||
| Total | 367 856 1223 |
Expected Table
| Gave advice Yes No | Total | |||
| Boys (600*367)/1223= 180.0 (600*856)/1223= 420.0 600 | ||||
| Girls (623*367)/1223= 187.0 (623*856)/1223= 436.0 623 | ||||
| Total |
367 856 1223
X2= (186-180)2/180+(181-187)2/187+(414-420)2/420+(442-436)2/436= 0.20+0.19+0.09+0.08= 0.56
Since 0.56<3.84, we conclude that there is no difference between the
- proportion of boys and girls who gave advice product for parents.
- Shopped at a mall
- Contingency Table
- Shopped at a mall yes no Total
- Boys 144 456 600
- Girls 262 361 623
- Total 406 817 1223
- Expected Table
- Shopped at a mall yes no Total
- Boys (600*406)/1223= 199.2 (600*817)/1223= 400.8 600
- Girls (623*406)/1223= 206.8 (623*817)/1223= 416.2 623
- Total 406 817 1223
- X2= (144-199.2)2/199.2+(262-206.8)2/206.8+(456-400.8)2/400.8+(361-416.2)2/416.2= 15.3+14.7+7.6+7.3= 44.9
- Since 44.9>3.84, there is a difference between the proportion of boys and girls who shopped at a mall.