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Sample analysis

Chapter 9

Question 11.29

 

  1. 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 systemContingency Table
Played a video game    Yes    No    TotalBoys    498    102    600Girls    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

Played a video game    yes    no    Total
Boys    (600*741)/1223=363.5    (600*482)/1223=236.7    600Girls    (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.

  1. Read a book for fun

Contingency Table

 

  1. Read a book for fun Yes    No    Total
  2. Boys 276    324    600
  3. Girls 324    299    623
  4. Total 600    623    1223
  5. Expected Table
  6. Read a book for fun Yes    No    Total
  7. Boys (600*600)/1223= 294.4    (600*623)/1223= 305.6    600
  8. Girls (623*600)/1223= 305.6    (623*623)/1223= 317.4    623
  9. Total 600    623    1223
  10. 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
  11. 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    NoTotal
Boys    186    414    600
Girls    181    442    623
Total    367    856    1223

Expected Table

Gave advice    Yes    NoTotal
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

  1. proportion of boys and girls who gave advice product for parents.
  2. Shopped at a mall
  3. Contingency Table
  4. Shopped at a mall yes    no    Total
  5. Boys 144    456    600
  6. Girls 262    361    623
  7. Total 406    817    1223
  8. Expected Table
  9. Shopped at a mall yes    no    Total
  10. Boys (600*406)/1223= 199.2    (600*817)/1223= 400.8    600
  11. Girls (623*406)/1223= 206.8    (623*817)/1223= 416.2    623
  12. Total 406    817    1223
  13. 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
  14. Since 44.9>3.84, there is a difference between the proportion of boys and girls who shopped at a mall.

  Remember! This is just a sample.

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